ELECTRIC CURRENT

ELECTRIC CURRENT

The electric current can be defined as the ordered flow of the charge.

The current through the area is defined as amount of the charge flowing through the area per unit time
if is the charge that flows through the area in time , then the current is given by

Current can be classified as

 Direct current: The current whose magnitude and the direction remains constant with time

 Transient Current: The current whose magnitude and the direction varies with time

Transient current is further classified as

Periodic Current and non- periodic current

Periodic current is the current whose magnitude and the

direction varies with the time but it repeats itself after fixed
time interval

Non -Periodic current is the current whose magnitude and the

direction varies with the time and do not repeats itself after
fixed time interval

The periodic current can be of many types most commonly is

the alternating current

The alternating current is the current whose magnitude and

the direction is varies according to sinusoidal function

The other examples of the periodic current are square wave,

triangular wave, saw tooth wave current

The value of the current at any time is called the instantaneous

value of the current

For the DC, Current is denoted by I

For the AC, Current is denoted by i

The SI unit of the current is Ampere defined as is coulomb per

second

We define, current is said to be one ampere is 1 coulomb charge is passed through the conductor in
one second

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The direction of current is taken in which positive charge carriers would move ( the conventional
current ), even if the actual charge carriers are negative and move up in the opposite direction
(direction of flow of the electrons )

1. How many electrons per second constitute a current of one milli ampere?
2. If the charge flowing through the conductor is given by q = 3t2+2t +2 C, what is the current at t= 3
sec?
3. If the current through the conductor is given by I = 2t3+3t2+5t +3. Calculate the amount of the
charge flowing through the conductor is 5 sec?

Average thermal velocity

When a conductor does not have a current through it, its conduction electrons move randomly or we
say in a zigzag way , such type of the motion is called Brownian motion , hence no net motion in any
direction, this velocity is called the average thermal velocity and the average thermal velocity of the
electrons is always is zero

Drift velocity

When the conductor has a current through in it, these electrons still
move randomly but they are drifted to the direction opposite to the
direction of applied electric field.

The average velocity with which the electrons are drifted toward
the positive terminal of the battery under the influence of external
electric field is called the drift velocity.

Consider a wire of the cross section area „A‟ and the length „L‟ and
let the electron 1 is moving with velocity ⃗ , electron 2 is moving
with velocity ⃗ , similarly the nth electron is moving with velocity
⃗ as the no voltage is applied across the conductor the average
drift velocity is zero

⃗ ⃗ ⃗
⃗

When the electric field is applied across the conductor the electron will experience the force opposite to
the electric field ⃗

⃗ & electrons will accelerate with the acceleration of ⃗

If the time between the two successive collisions of the electron 1 with the atoms or other electrons is
and for the electron 2 is similarly for the electron n the time is

The electrons will be accelerated till they collide with the other electrons or the atoms therefore the
velocity of the electron 1 is

for nth the electron it is

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⃗

Therefore the average final velocity of the electrons

⃗ ⃗ ⃗ ( )

The drift velocity of the electron is given by

⃗ ⃗ ⃗

⃗ ⃗ ⃗
As

( )
The term is known as the average relaxation time or mean free time and is represented as

The average relaxation time is a temperature dependent, as the

temperature of the conductor. If the temperature remains
constant then the average relaxation time remains constant

Defining the new term

The mobility of the electron then the drift velocity of the electrons ⃗

| |

Therefore we have magnitude of the drift velocity is directly proportional to the electric field

Relation between the drift velocity and the Current

If the length of the conductor is , Area of the cross section current flowing through it be , the
magnitude of the charge on the electron is and the number of electrons carriers per unit volume be .

Then the total charge in the conductor will be

( )

Let the charge carriers move with the drift velocity , then time
taken by the electrons to cross the length L, and the
current

Putting the valve of q and t in above equation

( )
and So
( )

We define the term as the current density which is the current flowing through the conductor per
unit cross section area .It is denoted by the

SI units of the current density is the A / m2

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Substituting the value of the drift velocity

( )⃗

( )⃗

( ) is the new term called conductivity of conductor It is represented by

As is the multiplication of the constant term with vector ⃗ hence the current density is a vector
quantity. It can be represented as the same way as Electric field is represented in the conductor. It
defines the flow of the charge at a particle point in the conductor and greater is the area of the cross
section lesser is the current density, where as the current is a scalar quantity, it represents the flow of
the charge in the conductor as whole. Current in the conductor has same value everywhere, where as
the current density is different, at different points of the conductor

A B C C

At point , the number of the electrons crossing through the conductor will be same as that of point B
and C. hence the current at each section is same but the cross sectional area at B is max. and at point C
it is minimum therefore the current density at point B is minimum and at point C it is maximum .

1. If the potential difference V applied across the conductor is increased to 2V. How will the drift
velocity of the electron changes?

Problem -1

Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 1.0 ×
10–7 m2 carrying a current of 1.5 A. Assume that each copper atom contributes roughly one conduction
electron. The density of copper is 9.0 × 103 kg/m3, and its atomic mass is 63.5 u

Solution

The direction of drift velocity of conduction electrons is opposite to the electric field direction

The drift speed

The density of conduction electrons, n is equal to the number of atoms per cubic meter (assuming one
conduction electron per Cu atom as is reasonable from its valence electron count of one).
A cubic meter of copper has a mass of 9.0 × 103 kg. Since 6.0 × 1023 copper atoms have a mass of 63.5 g

Hence

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Problem-2

Calculate the drift velocity of electrons in a copper wire with a diameter of 2.053 mm carrying a 20.0 A
current, given that there is one free electron per copper atom. The density of copper is 8.80 × 103 kg/m3
and the atomic mass of copper is 63.54

1. The electron drift speed is estimated to be only a few mm s–1 for currents in the range of a few
amperes? How then is current established almost the instant a circuit is closed?

Electric field is established throughout the circuit, almost instantly (with the speed of light) causing
at every point a local electron drift. Establishment of a current does not have to wait for electrons
from one end of the conductor travelling to the other end. However, it does take a little while for
the current to reach its steady value

2. The electron drift arises due to the force experienced by electrons in the electric field inside the
conductor. But force should cause acceleration. Why then do the electrons acquire a steady
average drift speed?

Each „free‟ electron does accelerate, increasing its drift speed until it collides with a positive ion of
the metal. It loses its drift speed after collision but starts to accelerate and increases its drift speed
again only to suffer a collision again and so on. On the average, therefore, electrons acquire only a
drift speed.

3. When electrons drift in a metal from lower to higher potential, does it mean that all the ‘free’
electrons of the metal are moving in the same direction?

By no means. The drift velocity is superposed over the large random velocities of electrons.

4. Are the paths of electrons straight lines between successive collisions (with the positive ions of
the metal) in the
(i) Absence of electric field,
(ii) Presence of electric field?

(i) In the absence of electric field, the paths are straight lines;
(ii) in the presence of electric field, the paths are, in general, curved

Problem 3:

Two conducting wires X and Y of same diameter but different materials are joined in series across a
battery. If the number density of electrons in X is twice than that in Y, then find the ratio of drift
velocity of electrons in the two wires.

Problem 4:
The number density of free electrons in a copper conductor is . How long does an
electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross section of the
wire is and it is carrying a current of 3.0 A.
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Resistance and Resistivity

As the current density in the conductor depends upon the electric field and the properties of the
materials, In general this dependence can be quite complex but for the some materials, especially the
metals at a given temperature, The current density is directly proportional to the E.

⃗
and the ratio of the magnitude of the E and J is constant,.

This relationship is called the OHM‟S Law.

But when OHM’S law is obeyed we are more interested in the total current in a conductor than the current
density and more interested in the potential difference between the conductors than the electric field because
current and the potential difference are much easier to measured than the current density and the electric field.

As we have
( )
Re arranging the above equation we have

( ) or ( )

[ ] ( )
( )

We say that the potential difference i.e. voltage across the

conductor is directly proportional to the current through the
conductor

The term ( ) is constant for the conductor, is called the

resistance of the conductor
It is denoted by R. The SI units of the resistance is ohms ( )

(Volts / Ampere)

This is known as the macroscopic form of the ohm‟s law

The resistance of the conductor across the two points is said to be one ohm if a current of 1A passing
through the conductor results in to the potential difference of 1 volt across the two points.

4. Graph showing the variation of current versus voltage for a material

GaAs is shown in the figure. Identify the region of
(i) negative resistance
(ii) where Ohm's law is obeyed.

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5. Two wires „A‟ and „B‟ are of the same metal and are of same length .Their areas of cross section are
in the ratio of 2:1 . If the potential difference is applied across each wire in turn ,what will be the
ratio of the current flowing in „A‟ and „B‟ ?

6. Mention the limitations of Ohm‟s law. Limitations of Ohm‟s law:

1. Ohm‟s law applicable only for good conductors.

2. Ohm‟s law applicable only, when the physical conditions like temperature, pressure and
tension remains constant.

3. Ohm‟s law is not applicable at very low temperature and very high temperature.

4. Ohm‟s law is not applicable for semiconductors, thermistors, vacuum tubes, discharge tubes.

Resistivity
Resistivity is defined as the reciprocal of the conductivity. It is represented by ;

Defining the specific resistance or the Resistivity

The specific resistance or the Resistivity of the material can be defined as the resistance of the material
having unit cross sectional area and unit length if

Variation of Resistivity with temperature

The relation between temperature and Resistivity for the copper and other metals is fairly linear over a
broad temperature range

For the engineering applications following empirical relation holds

( )

Where is the Resistivity at given temperature T is the Resistivity at reference temperature ( )

is the temperature coefficient of the Resistivity

7. If the temperature of a good conductor decreases how does the relaxation time of the electrons
in the conductor change?

As we have

When the temperature decreases , collisions decreases and thus relaxation time increases which in
turn decreases the resistivity.

This can be explained on the basis that as the temperature increases the rate of the collisions between
the electrons and the other atoms increases which decreases the mean relaxation time , hence the

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resistivity of the conductor increases , similarly the resistance of the material increases with the
increase in the temperature .

( )

The temperature coefficient of the resistance can be defined as

( )
( )

Units of the temperature coeff. is

Problem -5
The resistance of the platinum wire of a platinum resistance thermometer at the ice point is 5 Ω and at
steam point is 5.23 Ω. When the thermometer is inserted in a hot bath, the resistance of the platinum
wire is 5.795 Ω. Calculate the temperature of the bath.
Solution
Here
( )
( )
Hence

Problem-6
At room temperature (27.0 °C)the resistance of a heating element is 100 W. What is the temperature of
the element if the resistance is found to be 117 , given that the temperature coefficient of the material
of the resistor is 1.70 × 10–4 °C–1 . [NCERT]

Problem-7
A silver wire has a resistance of 2.1 at 27.5 °C, and a resistance of 2.7 at 100 °C. Determine the
temperature coefficient of resistivity of silver. [NCERT]

Problem-8
A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which
settles after a few seconds to a steady value of 2.8 A. What is the steady temperature of the heating
element if the room temperature is 27.0 °C? Temperature coefficient of resistance of nichrome averaged
over the temperature range involved is 1.70 × 10–4 °C–1. [NCERT]

Problem-9
A negligibly small current is passed through a wire of length 15 m and uniform cross-section 6.0 × 10–7
m2, and its resistance is measured to be 5.0 . What is the resistivity of the material at the temperature
of the experiment? [NCERT]

8. Why is the constantan or manganin used for making standard resistors?

The alloys such as constantan or manganin are used for making standard resistors because their
resistivities are high and has low temperature coefficient of resistance.

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9. What are the ohmic and non – ohmic resistors? Give one example of each.

ELECTRICAL ENERGY, POWER

Whenever the electric current is passed through a conductor, It becomes hot, which means electric
energy is converted heat energy.
Cause of the heating, as the potential difference is applied
across the conductor. A electric field is set up and
electrons gets accelerated towards the positive end hence
kinetic energy due to thermal motion and electric field
there will be collisions which will be in-elastic in nature
and energy which is not transferred in the collisions will
be transformed into heat .
Consider a conductor with end points A and B, in which a
current I is flowing from A to B.
The electric potential at A and B are denoted by ( ) and
( ) respectively. Since current is flowing from A to B,
( ) ( )
and the potential difference across AB is ( ) ( ) .
In a time interval , an amount of charge travels from A to B. The potential energy of the
charge at A, by definition, was ( ) and similarly at B, it is ( ).
Thus, change in its potential energy is

( ( ) ( )

If charges moved without collisions through the conductor, their kinetic energy would also change so
that the total energy is unchanged. Conservation of total energy would then imply that,

that is,

Thus, in case charges were moving freely through the conductor under the action of electric field, their
kinetic energy would increase as they move. We have, however, seen earlier that on the average,
charge carriers do not move with acceleration but with a steady drift velocity. This is because of the
collisions with ions and atoms during transit. During collisions, the energy gained by the charges thus
is shared with the atoms. The atoms vibrate more vigorously, i.e., the conductor heats up. Thus, in an
actual conductor, an amount of energy dissipated as heat in the conductor during the time interval
is,

Electric Power

The energy dissipated per unit time is the power dissipated

SI units of the power is watt

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Power of the circuit is said to be one watt if one ampere current flows against the potential difference
of 1 V
Using Ohm‟s law

This power loss is also known as ohmic loss in a conductor of resistance R carrying a current I. It is
this power which heats up, for example, the coil of an electric bulb to incandescence, radiating out heat
and light.

Electric Energy

The total work done or the energy supplied by the source of the emf in marinating the current in the
electric circuit for given time is called Electric Energy

Generally It is expressed in KWh

Total energy consumed when an electric appliance of power 1KW for 1 hours

( )

Efficiency of the Electric Device

It is denoted as

Problem -10
Refer to circuit shown. What will be the total power dissipation in
the circuit if P is the power dissipated in R1? It is given that R2=4R1
and R3=12R1

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Problem -11
A 220V and 100W lamp is connected to 220V power supply. What is the power consumed?

Problem -12
Two resistors of 6 and 9 are connected in series to a 120 volt source. What will be the power consumed by
the 6 resistor ?

Problem -13
A 25 watt, 220 volt bulb and a 100 watt, 220 volt bulb are connected in parallel across a 220 volt line. Which bulb
will glow more brighter?

Problem -14
A heating coil can heat the water of a vessel from 20 °C to 60 °C in 30 minutes. Two such heating coils are put in
series and then used to heat the same amount of water through the same temperature range. Find the new time
taken (neglecting thermal capacity of the coils)

Problem -15
A battery of e.m.f. 10 V and internal resistance 0.5 ohm is connected across a variable resistance R. For
what value of the value of R ,the power delivered in it is maximum?

Problem -16
Two wires 'A' and 'B' of the same material have their lengths in the ratio 1 : 2 and radii in the ratio 2 : 1.
The two wires are connected in parallel across a battery. What will be the ratio of the heat produced in
„A‟ to the heat produced in „B‟ for the same time ?

ELECTROMOTIVE FORCE

Cell : It is a device which provides the energy to the electrons in the conductor .

In the cell the influence that makes current flow from the lower to the higher potential is called
electromotive force ( abbreviated as emf) emf is not a force but an energy per unit charge quantity
( like potential )

Every complete circuit with steady current must include some device that provides emf, such device is
called source of the emf eg. Batteries, electric generators, solar cells etc.

All such devices convert energy of some form of (mechanical, chemical or other) into electric potential
energy and transfers it to the circuit to which device is connected

Schematic diagram of the ideal source of the emf that maintains the potential difference between the
conductors „A‟ and „B‟ called the terminals of the device

The terminal „A‟ is marked positive is maintained at higher potential than the terminal „B‟ marked
negative , associated with the potential difference is an
electric field E in the region around the terminals , both
inside and the outside the device . The electric field inside
the device is directed from „A‟ to „B‟

Charge „q‟ within the source experiences an electric force

but the source also

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provides an additional influence which we will represent as an non electrostatic force , This force
operating inside the device pushes the charge from „B‟ to „A‟ in an uphill direction against the electric
force . This maintains the potential difference between the terminals. If were not present
charge would flow between the terminals until the potential difference was zero.

The origin of the additional influence depends upon the kind of the source. In the generator it
results from the magnetic field force on the moving charges.
In the battery or the fuel cell it is associated with the diffusion process and the varying electrolyte
concentration resulting from the chemical reactions.

If the positive charge „q‟ is moved from the „B‟ to „A‟ inside the source , the non electrostatic force F n
does as positive work on the charge the displacement is opposite to the electrostatic force so
the potential energy associated with charge increases by
is the ( Positive ) potential of a point „a‟ with respect to „b‟ .

For an ideal source and are equal in magnitude but opposite in direction so that the total work
done is zero, there is increase in the potential energy but no change in the kinetic energy of the charge
is the increase in the potential energy is just equal to the non electrostatic work

Now let us make a complete circuit by connecting a wire resistance R to the terminals of the source
,The potential difference between the terminals „A‟ and „B‟ sets up an electric field with in the wire
.This causes current to flow around the loop from „A‟ to „B‟ from the higher potential to the lower
potential.

When the wire bends equal amount of the positive and the negative charges persists on inside and
outside of the bend. These charges exert the force that causes current to follow the bends in the wire.

It is common misconception that in a closed circuit, current is something that squirts out of the positive terminal
of the battery and consumed or ‘used up’ by the time it reaches the negative terminal but in fact the current is
same at each and every point in the simple loop even if the thickness of the wire is different at different points in
the circuit. This happens because the charge is conserved and the charge cannot be accumulated in the circuit. If
the charge did accumulate the potential difference would change with time.

Internal resistance

Real sources in the circuit don‟t behave in exactly the way we have described; the potential difference
across the real source in a circuit is not equal to the emf. The reason is that the charge moving through
the material of any real source encounters the resistance which we call the internal resistance of the cell
and some potential drop occurs across it and this internal resistance depends upon following
 Distance between the electrodes
 The nature of the electrolyte
 The nature of the electrodes, and
 The area of the electrodes
 Temperature of the electrolyte

Hence we get a less terminal potential difference of the cell which is less than the emf (electromotive
force which is the cause of the electric current in the circuit).
It is denoted by a series resistance.

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is the emf of the cell; V is the potential drop across the load
resistance
( )

( )

Relation between the electromotive force and the Potential

drop
or ( )

Or the internal resistance can be written as

( )
or ( )

Cells in series
Consider two cell connected in series, with negative terminal of one cell is connected to the positive
terminal of the other.

Let , are the emf‟s of the two cells. , are the internal resistances of the cells. „I‟ be the current
sent by the cells.

Let , and be the potentials at points A, B and C respectively.

The potential difference between the positive and negative terminals of the first cell is
. The potential difference between the positive and negative terminals of the
second cell is . The potential difference between the terminals A and C of the
combination is
( ) ( ) ( ) ( )

Hence
( ) ( ( )) -------1

The series combination of two cells can be replaced by a single cell between „A‟ and „C‟ of emf
and internal resistance ,

---------- (2)

Comparing equations (1) and (2)

and

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Cells in parallel

Consider two cell connected in Parallel,

Let and are the emf‟s of the two cells. and are the internal resistances of the cells connected
in parallel across points and . and are the currents leaving the positive electrodes of the cells.
At the point , and flow in whereas the current „I‟ leave out.

Let ( ) and ( ) be the potentials at and , respectively.

For the first cell, The potential difference across its terminals is ( ) ( ).

Points and are connected exactly similarly to the second cell. Hence considering the second cell,
we also have

Points and are

connected exactly similarly to
the second
cell. Hence considering the
second cell, we also have
( ) ( ).

( )

( )

( )
-----1
( ) ( )

If we want to replace the combination by a single cell, between and , of emf and internal
resistance we would have

( )

( )

( )

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Grouping of cells:

a. Grouping in series: If „n‟ cells each of emf and internal resistance „r‟ are connected in series
with an external resistance R then

When
i.e. the current will maximum when the external resistance is much more than internal
resistance.

b. Grouping in parallel: If „m‟ cells each of emf and internal resistance „r‟ are connected in parallel
with the external resistance R then

( )

When

i.e. the current will maximum when the internal resistance is much more than external
resistance.

c. Mixed grouping: If „n‟ cells each of emf and internal resistance „r‟ are connected in series and
„m‟ such sets are connected in parallel and the combination is connected in series with an external
resistance R then

When
i.e. the current will maximum when the external resistance is equal to the internal resistance.

 If n cells of emf are connected in series then the effective emf will be given by
and if they are connected in parallel then the effective emf will be

Internal Resistance Of a Cell (r): It is the resistance offered by the electrolyte to the flow of current in
the cell.
( )
„
It depends on the following factors:
a) Distance between the electrodes: Internal resistance of the cell increases with increase in the
distance between the plates of the cell.
b) Concentration of the electrolyte: Internal resistance of the cell increases with increase in the
concentration of the electrolyte.
c) Area of electrodes: Internal resistance of the cell decreases with increase in the area of the plates
of the cell.
d) Polarization in the cell: Greater the polarization, greater the internal resistance.
e) Temperature: On increasing the temperature, internal resistance decreases.

Open Circuit: It means no current is being drawn from the cell, terminal potential difference is equal to
the emf of the cell.
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Closed Circuit: It means current is being drawn from the cell, the terminal
potential difference across the cell is less than the e.m.f of the cell, cell is
being discharged.

Short Circuit: It means maximum current is drawn from the source , the terminal potential difference is
zero.

During the charging of the cell , terminal potential difference is greater than the emf of the cell. The
current flows in the cell ,

10. A low voltage supply from which one needs high current must have very low internal resistance.
Why?
Since the maximum current drawn from the source is so for the low value of the internal
resistance current will be high.

11. Is there a net electric field inside the cell when the circuit is closed and a steady current passes
through? Explain.
When the circuit is closed from the outside the current flows in the direction of the electrostatic
field outside, and opposite to the direction of the electro static field inside the cell.So we can say
there is a net field inside the cell opposite to the electrostatic field.

12. Terminal potential difference is less than the emf of a cell. Why?

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When circuit is open,the terminal potential difference is equal to emf of the cell . When current is
drawn from the cell, some potential drop takes place due to internal resistance of the cell. Hence
terminal potential difference is less than the emf of a cell and is given by

Problem -17
The storage battery of a car has an emf of 12 V. If the internal resistance of the battery is 0.4 , what is
the maximum current that can be drawn from the battery? [NCERT]

Problem-18
An ammeter together with an unknown resistance in series is connected across two identical batteries
each of emf 1.5 V. When the batteries are connected in series, the ammeter records a current of 1A and
when the batteries are in parallel, the current is 0.6A. What is the internal resistance of each battery?

Problem-19
A storage battery has an emf of 8.0 V and internal resistance of 0.5 is allowed by charged by a 120 V,
DC supply using a series resistor of 15.5 . What is the terminal voltage of the battery during charging?
What is the purpose of having a series resistor in the charging circuit? [NCERT]

Problem -20
Two identical cells, each of emf E, having negligible internal resistance, are connected in parallel with
each other across an external resistance R. What is the current through this resistance ?

Problem -21
A battery of emf 10 V and internal resistance 3 W is connected to a resistor. If the current in the circuit
is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the
circuit is closed? [NCERT]

KIRCHHOFF’S LAWS

Electrical Circuit: Circuit can be defines the closed path in which the current can flow.

Junction: It is the point in the circuit at which the current divides it self

JUNCTION LAW states that algebraic sum of the currents meeting at a

junction is zero (incoming current is equal to outgoing current).

This is in accordance with the conservation of the charge. The equating of the continuity, all the
charges enter a given point must leave that point because
the charge cannot build up at a point, we can think the
above thing same as the flow of the water, the water flows
through the branched pipe , in which the flow rate into
the pipe equals the total flow rate out of the two branches
of the pipe

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VOLTAGE LAW states that for any closed path of electrical circuit, the algebraic sum of all the
potential differences is equal to zero
∑

This law is in accordance with the conservation of

energy .Let us imagine moving a charge around t he
closed loop of the circuit . When the charge returns at
the starting point, the charge –circuit system must
have same potential energy as it had before the
charge was moved. The sum of increases in the
energy as charge passes through some circuit
elements must equal the sum of the decreases in the
energy as it passes through the other elements

 The potential difference (potential drop) will be taken as positive if we move from higher
potential to lower potential.
 It will be taken as negative if we move from lower potential to higher potential.

In the closed loop abcdefa V1 +V2 + V3 – E = 0

IR1 +IR2 + IR3 – E = 0

While applying Kirchhoff‟s second rule, we imagine travelling around the loop and consider the
changes in the electric potential, this law can be written in for of the changes in the electric potential, or
in form of the potential drop across the loop.

We must use the following conventions while using the second law

 because the charges move from the high potential end of the
resistor towards the low potential end , if the resistor is
traversed in the direction of the current , the potential drop is
taken as IR ( change in potential will be taken as –IR)

 if the resistor is traversed in the direction opposite to the

current , the potential drop is taken as -IR ( change in
potential will be taken as IR)

 If the source of emf has zero internal resistance is traversed in the

direction of the emf ( - to +) , the potential drop is taken as -E (
change in potential is taken as E)

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ELECTRIC CURRENT
 If the source of emf has zero internal resistance is traversed in the direction opposite to the emf (
+ to -) , the potential drop is taken as E ( change in potential is
taken as -E)

 In order to solve a particular circuit problem , the number of the independent equations we need
to obtain the two rules equals to the number of unknown currents

 Any capacitor acts as an open branch in the circuit

Problem -22
Using Kirchhoff‟s laws, find the value of currents I1, I2 and I3 in the circuit diagram shown below

Problem -23
A battery of 10 V and negligible internal resistance is connected across
the diagonally opposite corners of a cubical network consisting of 12
resistors each of resistance 1 Ω . Determine the equivalent resistance of
the network and the current along each edge of the cube. [NCERT]

Problem-24
Determine the current in each branch of the network shown in Fig. [NCERT]

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ELECTRIC CURRENT
Problem-25
Use Kirchhoff‟s rules to determine the potential difference between the points A and D when no
current flows in the arm BE of the electric network shown in the figure. [NCERT]

WHEAT STONE BRIDGE PRINCIPLE

Wheat stone bridge principle states if four resistances are connected in form of bridge with a cell at
connected at opposite corners of the bridge and at other two corners the galvanometer is connected,
bridge is said to be balanced if no current flows through the
galvanometer

Let be he current flowing through the circuit, I1 be the current

through P,
( ) be the current through R, be the current flowing
through Galvanometer, ( ) be the current flowing through Q
and
( ) be the current flowing through S , G is the
galvanometer resistance

Applying the Kirchhoff‟s law to left hand closed loop

( )
Applying the Kirchoff‟s law to left hand closed loop
( ) ( )

The value of the resistance R is adjusted so that no current flows through the

Galvanometer

( ) or ( )

( ) ( )

Therefore we have

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ELECTRIC CURRENT

Meter Bridge

It consists of a wire of length 1m and of uniform cross sectional area stretched taut and clamped
between two thick metallic strips bent at right angles, as shown. The metallic strip has two gaps across
which resistors can be connected. The end points where the wire is clamped are connected to a cell
through a key. One end of a galvanometer is connected to the metallic strip midway between the two
gaps. The other end of the galvanometer is connected to a „jockey‟. The jockey is essentially a metallic
rod whose one end has a knife-edge which can slide over the wire to make electrical connection.

R is an unknown resistance whose value we want to determine. It is connected across one of the gaps.
Across the other gap, we connect a standard known resistance S. The jockey is connected to some point
D on the wire, a distance l cm from the end A. The jockey can be moved along the wire. The portion
AD of the wire has a resistance Rcml, where Rcm is the resistance of the wire per unit centimetre. The
portion DC of the wire similarly has a resistance Rcm (100-l ). The four arms AB, BC, DA and CD form a
Wheatstone bridge with AC as the battery arm and BD the galvanometer arm. If the jockey is moved
along the wire, then there will be one position where the galvanometer will show no current. Let the
distance of the jockey from the end A at the balance point be l= l1. The four resistances of the bridge at
the balance point then are R, S, Rcm l1 and Rcm(100–l1). The balance condition,

( ) ( )

or
( )
( )

Problem -26

The four arms of a Wheatstone bridge have the following

resistances: AB = 100Ω, BC = 10Ω, CD = 5Ω, and DA = 60Ω
A galvanometer of 15Ω resistance is connected across BD. Calculate
the current through the galvanometer when a potential difference of
10 V is maintained across AC. [NCERT]

Problem -27
In a meter bridge the null point is found at a distance of 33.7 cm
from A. If now a resistance of 12Ω is connected in parallel with S,
the null point occurs at 51.9 cm. Determine the values of R and S.

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ELECTRIC CURRENT
13. Why are the connecting resistors in a meter bridge made of thick copper strips?

Thick copper strips offer minimum resistance and hence avoid the error due to end resistance
which have not been taken in to account in the meter bridge formula

14. What happens if the galvanometer and the cell are interchanged at the balance point of the
bridge ?

15. Wheat stone bridge is unsuitable for the measurement of very high resistance. Why?

Assignment

1. How is the electric field applied along the length of the conductor?

2. Why is the drift velocity of the electrons small?

3. Draw the graph to show the variation of the resistance of the metal wire as function of its diameter,
keeping the length and temperature constant?

4. A rectangular block of the iron has dimensions . What is the resistance of the block
measured between the two square ends? Given

5. For a cell the potential difference is less than the electro motive force .why ?

6. Why is it easier to start the car engine on a warm day than on the chilly day?

7. Under what circum stance the terminal potential difference of the battery exceeds the emf ?

8. Under what conditions is the series combination of cells is useful?

9. Under what conditions is the parallel combination of cells is useful?

10. When the Wheatstone bridge is most sensitive?

11. If the current flowing in the iron bar be allowed to flow through the another iron bar having
double the radius, then what will be the effect in the drift velocity of the electrons?

12. Two wires of same material having diameters in the ratio 2:3 are connected in series with a battery.
What is the ration of the voltages across the two wires if their lengths are in ratio 1:2?

13. A wire of resistance 4R is bent in form of circle. What is the effective resistance between the ends of
the diameter?

14. Why is the electric power transmitted at high voltage?

15. When the electric heater is switched on, an bulb in parallel becomes dim. Dimness becomes less
after some time. Why?

16. Why the brightness of the light emitted by the bulb decreases after some time?

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ELECTRIC CURRENT

17. Prove that if two resistances are connected in parallel, the rates of the heat production in each vary
inversely as their resistances ?

18. Name two physical conditions on which the resistivity of the metal depends?

19. Write two precautions you would observe while performing the experiment involving the meter
bridge?

20. The electron drift arise due to the force experienced by the electrons in the electric field inside the
conductor. But the force should cause acceleration. why then do the electrons acquire a steady
velocity?

21. In the figure , AB is one meter long uniform wire of

resistance. Other data are shown in the diagram. Calculate
a. Potential gradient along AB.
b. Length AO , when galvanometer shows no
deflection

Previous year questions

1. The plot of the variation of potential difference across a combination of

three identical cells in series, versus current is as shown in the figure. What
is the emf of each cell? (Delhi 2008)

2. Two conducting wires X and Y of same diameter across a battery. If the

number density of electro in X is twice that in Y, find the ratio of drift velocity of electrons in the
two wires. (All India 2008)

3. When electrons drift in a metal from lower to higher potential, does it mean that all the free
electrons of the metal are moving in the same direction? (Delhi 2012)

4. Two wires of equal length, one of copper and the other of manganin have the same resistance.
Which wire is thicker? (All India 2012)

5. A 10 V battery of negligible internal resistance is connected across a

200 V battery and a resistance of 38Ω as shown in the figure. Find the
value of the current in circuit. (Delhi 2013)

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ELECTRIC CURRENT

6. A 5 V battery of negligible internal resistance is connected across a 200

V battery and a resistance of 39 Ω as shown in the figure. Find the
value of the current (Delhi 2013)

7. The emf of a cell is always greater than its terminal voltage. Why? Give reason.
(Delhi 2013)

8. Why is the terminal voltage of a cell less than its emf?

(Comptt. All India 2013)
9. Two students A and B were asked to pick a resistor of 15 kΩ from a collection of carbon resistors. A
picked a resistor with bands of colours : brown, green, orange while B chose a resistor with bands
of black, green, red. Who picked the correct resistor? (Comptt. All India 2013)

10. Define the term „Mobility‟ of charge carriers in a conductor. Write its S.I. unit.
(Delhi 2014)
11. Show variation of resistivity of copper as a function of temperature in a graph.
(Delhi 2014)
12. Define the term „electrical conductivity‟ of a metallic wire. Write its S.I. unit.
(Delhi 2014)
13. Define the term „drift velocity‟ of charge carriers in a conductor and write its relationship with the
current flowing through it. (Delhi 2014)

14. How does the random motion of free electrons in a conductor get affected when a potential
difference is applied across its ends? (Comptt. Delhi 2014)

15. Write the expression for the drift velocity of charge carriers in a conductor of length T across which
a potential difference „V‟ is applied. (Comptt. All India 2014)

16. How does one explain increase in resistivity of a metal with increase of temperature?
(Comptt. All India 2014)

17. A cell of emf 'E' and internal resistance 'r' is connected across a variable load resistor R. Draw the
plots of the terminal voltage V versus (i) R and (ii) the current I. It is found that when R = 4 , the
current is 1 A and when R is increased to 9 , the current reduces to 0.5 A. Find the values of the
emf E and internal resistance r. (All India 2014)

18. The plot of the variation of potential difference A across a combination of three identical cells in
series, versus current is shown along the question. What is the emf and internal resistance of each
cell? (All India 2016)

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ELECTRIC CURRENT
19. Nichrome and copper wires of same length and same radius are connected in series. Current I is
passed through them. Which wire gets heated up more? Justify your answer.
(Outside Delhi 2017)

20. Two metallic wires of the same material have the same length but cross-sectional area is in the ratio
1 : 2. They are connected
(i) in series and
(ii) in parallel. Compare the drift velocities of electrons in the two wires in both the cases (i) and (ii).
(All India 2008)
21. Derive an expression for the resistivity of a good conductor, in terms of the relaxation time of
electrons. (All India 2008)

22. Using the mathematical expression for the conductivity of a material, explain how it varies with
temperature for
(i) semiconductors,
(ii) good conductors. (All India 2008)

23. A cell of emf „E‟ and internal resistance V is connected across a variable resistor „R‟. Plot a graph
showing the variation of terminal potential „V‟ with resistance R.
Predict from the graph the condition under which „V‟ becomes equal to „E‟. (Delhi 2009)

24. Derive an expression for drift velocity of free electrons in a conductor in terms of relaxation time.
(Delhi 2009)
25. Calculate the current drawn from the battery in the given network.

(All India 2009)

26. A wire of 20 Ω resistance is gradually stretched to double its original length. It is then cut into two
equal parts. These parts are then connected in parallel across a 4.0 volt battery. Find the current
drawn from the battery.
(All India 2009)
27. In the given circuit, assuming point A to be at zero potential, use Kirchhoff‟s rules to determine the
potential A at point B.

(All India 2011)

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ELECTRIC CURRENT
28. In the meter bridge experiment, balance point was observed at J with AJ = l.

(i) The values of R and X were doubled and then interchanged. What would be the new position
of balance point?
(ii) If the galvanometer and battery are interchanged at the balance position, how will the balance
point get affected? (All India 2011)

29. The network PQRS, shown in the circuit diagram, has the batteries of 4 V and 5 V and negligible
internal resistance. A milliammeter of 20 Ω resistance is connected between P and R. Calculate the

reading in the milliammeter.

(Comptt. All India 2012)

30. A cell of emf „E‟ and internal resistance V is connected across a variable resistor „R‟. Plot a graph
showing variation of terminal voltage „V‟ of the cell versus the current „I‟. Using the plot, show how
the emf of the cell and its internal resistance can be determined.
(All India 2014)

31. Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 2.5
× 10-7 m2 carrying a current of 1.8 A. Assume the density of conduction electrons to be 9 × 1028 m-3.
(All India 2014)

32. Distinguish between emf (ε) and terminal voltage (V) of a cell having internal resistance r. Draw a
plot showing the variation of terminal voltage (V) vs the current (I) drawn from the cell. Using this
plot, how does one determine the internal resistance of the cell?
(Comptt All India 2014)

33. Two cells of emfs 1.5 V and 2.0 V having internal resistance 0.2 Ω and 0.3 Ω respectively are
connected in parallel. Calculate the emf and internal resistance of the equivalent cell.
(Delhi 2016)
34. Two electric bulbs P and Q have their resistances in the ratio of 1 : 2. They are connected in series
across a battery. Find the ratio of the power dissipation of these bulbs
(All India 2018)

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ELECTRIC CURRENT
35. A 10 V cell of negligible internal resistance is connected in parallel across a battery of emf 200 V and
internal resistance 38 as shown in the figure. Find the value of current in the circuit

(All India 2018)

36. (a)Define the term 'conductivity' of a metallic wire. Write its SI unit.
(b) Using the concept of free electrons in a conductor, derive the expression for the conductivity of
a wire in terms of number density and relaxation time. Hence obtain the relation between
current density and the applied electric field E.
(All India 2018)
37. How does the mobility of electrons in a conductor change, if the potential difference applied across
the conductor is doubled, keeping the length and temperature of the conductor constant ?
(All India 2019)

38. Two bulbs are rated (P1, V) and (P2, V). If they are connected (i) in series and (ii) in parallel across a
supply V, find the power dissipated in the two combinations in terms of P1 and P2.
( All India 2019)
39. Using Kirchhoff‟s rules, calculate the current through the 40 and 20 resistors in the following
circuit

40. What is end error in a metre bridge ? How is it overcome ? The resistances in the two arms of the
metre bridge are R = 5 and S respectively.

When the resistance S is shunted with an equal resistance, the new balance length found to be 1.5 l1,
where l1 is the initial balancing length. Calculate the value of S.
( All India 2019)

41. Two resistors R1 and R2 of 4 and 6 are connected in parallel across a battery. The ratio of power
dissipated in them, P1 : P2 will be
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ELECTRIC CURRENT
(A) 4:9 (B) 3:2 (C) 9:4 (D)
2:3
(All India 2020)
42. Explain the principle of working of a meter bridge. Draw the circuit diagram for determination of
an unknown resistance using it.
(All India 2020)

43. .
(a) Two cells of emf E1 and E2 have their internal resistances r1 and r2, respectively. Deduce an
expression for the equivalent emf and internal resistance of their parallel combination when
connected across an external resistance R. Assume that the two cells are supporting each other.
(b) In case the two cells are identical, each of emf E = 5 V and internal resistance r = 2 , calculate the
voltage across the external resistance R = 10 .
(All India 2020)

44. A current of 0.8 flows in a conductor of 40 for 1 minute. The heat produced in the conductor
will be.
a. 1445 b. 1536 c. 1569 d. 1640 J
(All India 2023)

45. A cell of emf E is connected across an external resistance R. When current „I‟ is drawn from the
cell, the potential difference across the electrodes of the cell drops to V. The internal resistance „r‟
of the cell is

a. ( ) b. ( ) c. ( ) d. ( )

(All India 2023)

46. Define current density and relation time. Derive an expression for resistivity of a conductor in
terms of number density of charge carries in the conductor and relaxation time
(All India 2023)

47. Electrons drift with speed vd in a conductor with potential difference V across its ends .If the V is
reduced to V/2 , their drift speed will become
a. b. c. d.
(All India 2024)
48.
(a) “the electron drift speed is only a few mm/s for the currents in the range of a few
ampere for a given conductor” How then is the current established almost the instant a
circuit is closed ? Explain?
(b) „V=IR is a statement of Ohms law‟ is not true .Explain (All India 2024)

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ELECTRIC CURRENT
49. The figure shows a circuit with three ideal batteries .Find the magnitude and the direction of the
current in the branches AG, BF and CD.

(All India 2024)

50. When the terminal of a cell are connected to a conductor of resistance R, an electric currnet flows
through the circuit. The electrolyte of the cell also offers some resistance in the path of the current
, like the conductor . This resistance offered by electrolyte us called internal resistance of the cell (
r) .It depends upon the nature of the electrolyte , the area of the electrodes immersed in the
electrolyte and the temperature .Due to the internal resistance , a part of energy supplied by the
cell is wasted in the form of heat.
When no current is drawn from the cell , the potential difference between the two the electrodes
is known as the emf of the cell ( )With a current drawn from the cell the potential difference
between the two the electrodes of terminal potential difference (V)
(i) Choose the in-correct statement
(a) The potential difference (V) between the two terminals of the cell in the closed
circuit is always less that its emf ( )of the cell during the discharging of the cell.
(b) The internal resistance of the cell decreases with the decrease in the temperature
of the electrolyte.
(c) When the current is drawn from the cell then .
(d) The graph between the potential difference between the two terminals of the cell
(V) and the current (I) through it is a straight line with negative slope.

(ii) Two cells of emf 2.0 V and 6.0 V and the internal resistance 0.1 and 0.4 respectively,
are connected in the parallel . The equivalent emf of the combination will ve
(a) 2.0V (b) 2.8 V (c) 6.0V (d) 8.0 V

(iii) Dipped in the solution , the electrolyte exchange charges with the electrolyte. The
positive electrode develops the a potential difference V+(V+>0), and the negative
electrode develops a potential -V_ ( V_>0), relative the electrolyte adjacent to it .When
no current is drawn from the cell then ,
(a) (b)
(c) (d)

(iv) Five identical cells, each of emf 2V and internal resistance 0.1 are connected in
parallel. This combination in turn is connected to external resistor of 9.98 .The current
flowing through the resistor is
(a) 0.05 A (b) 0.1 A (c) 0.15 A (d) 0.2A
OR

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ELECTRIC CURRENT
Potential difference across the cell in the open circuit is 6V. It becomes 4V when a
current of 2A is drawn from it The internal resistance of the cell is
(a) 1.0 (b) 1.5 (c) 2.0 (d) 2.5
(All India 2024)

NCERT- Exemplar

1. Consider a current carrying wire in the shape of a circle. Note that as the current progresses along
the wire, the direction of j changes in an exact manner, while the current I remain unaffected. The
agent that is essentially responsible for is
a. source of emf.
b. electric field produced by charges accumulated on the surface of wire.
c. the charges just behind a given segment of wire which push them just the right way by
repulsion.
d. the charges ahead .

2. Two batteries of emf ε1 and ε2 and internal resistances r1 and r2 respectively are connected in
parallel as shown in the figure.

a. the equivalent emf εeq of the two cells is between ε1 and ε2 that is
ε1 < εeq < ε2
c. the equivalent emf εeq is smaller than ε1
c. the εeq is given by εeq = ε1 + ε2 always
d. εeq is independent of internal resistances r1 and r2.

3. A resistance R is to be measured using a meter bridge. Student chooses the standard resistance S
to be 100 . He finds the null point at l1 = 2.9 cm. He is told to attempt to improve the accuracy.
Which of the following is a useful way?
a. he should measure l1 more accurately.
b. he should change S to 1000 and repeat the experiment.
c. he should change S to 3 and repeat the experiment.
d. he should give up hope of a more accurate measurement with a meter bridge.

4. Two cells of emf‟s approximately 5V and 10V are to be accurately compared using a
potentiometer of length 400 cm.
a. the battery that runs the potentiometer should have voltage of 8V.
b. the battery of potentiometer can have a voltage of 15V and R adjusted so that the
potential drop across the wire slightly exceeds 10V.
c. the first portion of 50 cm of wire itself should have a potential drop of 10V.
d. potentiometer is usually used for comparing resistances and not voltages.

5. A metal rod of length 10 cm and a rectangular cross-section of 1 cm × 1/2 cm is connected to

battery across opposite faces. The resistance will be
a. maximum when the battery is connected across 1 cm × 1/2 cm faces.
b. maximum when the battery is connected across 10 cm × 1 cm faces.
c. maximum when the battery is connected across 10 cm × 1/2 cm faces.
d. same irrespective of the three faces.

6. Which of the following characteristics of electrons determines the current in a conductor?

a. drift velocity alone.
b. thermal velocity alone.

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ELECTRIC CURRENT
c. both drift velocity and thermal velocity.
d. neither drift nor thermal velocity.

7. Kirchhoff‟s junction rule is a reflection of

a. conservation of current density vector.
b. conservation of charge.
c. the fact that the momentum with which a charged particle approaches a junction is
unchanged as the charged particle leaves the junction.
d. the fact that there is no accumulation of charges at a junction.

8. Consider a simple circuit in the figure. stands a for variable resistance R‟. R‟ can vary
from R0 to infinity. r is internal resistance of the battery.

a. potential drop across AB is nearly constant as R‟ is varied.

b. current through R‟ is nearly a constant as R‟ is varied.
c. current I depends sensitively on R‟
d. always.

9. Temperature dependence of resistivity ρ(T) of semiconductors, insulators, and metals is

significantly based on the following factors:
a. number of charge carriers can change with temperature T.
b. time interval between two successive collisions can depend on T.
c. length of material can be a function of T.
d. mass of carriers is a function of T.

10. The measurement of an unknown resistance R is to be carried out using Wheatstone bridge. Two
students perform an experiment in two ways. The first student take R2 = 10 and R1 = 5 . The
other student takes R2 = 1000 and R1 = 500 . In the standard arm, both take R3 = 5 . Both find
( ) within errors.
a. the errors of measurement of the two students are the same.
b. errors of measurement do depend on the accuracy with which R2 and R1 can be
measured.
c. if the student uses large values of R2 and R1, the currents through the arms will be
feeble. This will make determination of null point accurately more difficult.
d. Wheatstone bridge is a very accurate instrument and has no errors of measurement.

11. In a meter bridge the point D is a neutral point.

a. the meter bridge can have no other neutral point

for this set of resistances.
b. when the jockey contacts a point on meter wire
left of D, current flows to B from the wire.
c. when the jockey contacts a point on a meter wire
to the right of D, current flows from B to the wire
through galvanometer.
d. when R is increased, the neutral point shifts to left.

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ELECTRIC CURRENT

Ans

1. b 2. a 3. c 4. b 5. a
6. a 7. b,d 8. a,d 9. a,d 10. b,c
11. a,c

12. Is the momentum conserved when charge crosses a junction in an electric circuit? Why or why
not?
The momentum is not conserved when the charge crosses a junction in an electric circuit. This is
because the drift velocity is proportional to the electric field.

13. The relaxation time τ is nearly independent of applied E field whereas it changes significantly
with temperature T. First fact is responsible for Ohm’s law whereas the second fact leads to
variation of ρ with temperature. Elaborate why?
Relaxation time is the time interval between two successive collision of the electrons.
It is defined as
τ = mean free path/rms velocity of electrons
Usually the drift velocity of the electrons is small because there is a frequent collision between the
electrons.

14. What are the advantages of the null-point method in a Wheatstone bridge? What additional
measurements would be required to calculate R unknown by any other?
The advantage of a null-point in the Wheatstone bridge is that the resistance of the galvanometer
is not affected by the balance point. The R unknown is calculated by using Kirchhoff‟s rule.

15. For wiring in the home, one uses Cu wires or Al wires. What considerations are involved in
this?
The main considerations in selection of the wires is conductivity of the metal, cost of metal, and
their availability.

16. Why are alloys used for making standard resistance coils?
Alloys are used in making of the standard resistance coils because they have less temperature
coefficient of resistance and the temperature sensitivity is also less.

17. Power P is to be delivered to a device via transmission cables having resistance Rc. If V is the
voltage across R and I the current through it, find the power wasted and how can it be reduced.
Power consumed by the transmission lines is given as P = i2Rc
Where Rc is the resistance of connecting cables
Power is given as P = VI
The transmission of power takes places either during low voltage and high current or during
high voltage and low current.

19. First a set of n equal resistors of R each are connected in series to a battery of emf E and
internal resistance R. A current I is observed to flow. Then the n resistors are connected in
parallel to the same battery. It is observed that the current is increased 10 times. What is ‘n’?
When the resistors are in series combination, current is given as .

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ELECTRIC CURRENT

When the resistors are in parallel combination, current is given as .

( )
Solving the two equations, we get n = 10.

20. Two cells of same emf E but internal resistance r1 and r2 are
connected in series to an external resistor R. What should be the
value of R so that the potential difference across the terminals of the
first cell becomes zero?

21. Two conductors are made of the same material and have the same length. Conductor A is a
solid wire of diameter 1 mm. Conductor B is a hollow tube of outer diameter 2 mm and inner
diameter 1 mm. Find the ratio of resistance RA to RB?

22. Two cells of voltage 10V and 2V and internal resistances 10Ω and 5Ω respectively are
connected in parallel with the positive end of the 10V battery connected to negative pole of 2V
battery. Find the effective voltage and effective resistance of the combination.

23. A room has AC run for 5 hours a day at a voltage of 220V. The wiring of the room consists of
Cu of 1 mm radius and a length of 10 m. Power consumption per day is 10 commercial units.
What fraction of it goes in the joule heating in wires? What would happen if the wiring is
made of aluminium of the same dimensions?

24. a. Consider circuit in the figure. How much energy is absorbed by electrons from the initial
state of no current to the state of drift velocity?

b. Electrons give up energy at the rate of RI2 per second to the thermal energy. What time
scale would one associate with energy in problem ‘a’ n = no of electron/volume = 1029/m3,
length of circuit = 10 cm, cross-section = A = 1mm2.

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ELECTRIC CURRENT

Multiple choice questions

1. A silver wire has a resistance of 2.1 Ω at 27.5 °C, and a resistance of 2.7 Ω at 100 °C. What is the
temperature coefficient of resistivity of silver?
a. 0.0059 b. 0.0039 c. 0.0129 d. 0.0159

2. Give the number of electrons passing through a wire per minute. The current flowing through
it is 500mA.
a. 1.875 × 1020 b. 6.875 × 1020 c. 1.875 × 10-20 d. 6.875 × 10-20

3. Identify the correct statement from the following about discharging of a cell.
a. The direction of current in the cell is from positive to negative terminal.
b. Terminal potential difference is greater than emf of the cell.
c. Terminal potential difference is lesser than emf of the cell.
d. The current increases and decreases frequently.

4. A cell has an emf of 6V, internal resistance of 1 ohms and a current of 0.5 A passing through it.
This cell is connected to a resistor. Find out the resistance of the resistor.
a. 10 b. 11 c. 12 d. 13

5. Two resistances are connected in two gaps of Meter Bridge. The balance is 20cm from the zero
end. A resistance of 15 ohms is connected in series with the smaller of the two. The null point
shifts to 40cm. What is the value of the bigger resistance (ohm)?
a. 9 b. 18 c. 27 d. 36

6. A resistance of 5 ohms is connected across the gap of a Meter Bridge and an unknown
resistance, greater than 5 ohms, is connected across the other gap. When these resistances are
interchanged, the balance point shifts by 50 cm. Neglecting any correction, what is the
unknown resistance (ohm)? The length of the wire is 150 cm.
a. 3 b. 10 c. 7 d. 5

7. Drift velocity of a free electron inside a conductor is:

a. the thermal speed of the free electron.
b. the average speed required by the electron in any direction.
c. the speed with which a free electron emerges out of the conductor.
d. the average speed of the electron between successive collisions in the direct opposition to
opposite to the applied electric field.

8. If potential difference V has been applied to a copper wire and the potential difference is
increased to 2V, the drift velocity of electrons will

a. be half the initial velocity. b. remain same.

c. be √2 times the initial velocity. d. be double the initial velocity.

9. The current in a wire varies with time according to the equation, , where, i is an
ampere and t is in second. The quantity of charge which has to be passed through a cross-
section of the wire during the time t =2s to t = 6s is:
a. 40 C b. 48 C c. 38 C d. 43 C

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10. The voltage V and current l graphs for a conductor at two different
temperatures T1 and T2 are shown in the figure. The relation between T1
and T2 is

a. T1 > T2 b. T1 < T2
c. T1 = T2 d.

11. In the diagram shown, the reading of voltmeter is 20 V and that of

ammeter is 4 A. The value of R should be (Consider given ammeter
and voltmeter are not ideal)
a. equal to 5 . b. greater than 5 .
c. less than 5 . d. greater or less than 5 .

12. When there is an electric current through a conducting wire along its length, then an electric
field must exist
a. outside the wire but normal to it. b. outside the wire but parallel to it.
c. inside the wire but parallel to it. d. inside the wire but normal to it.

13. A copper wire is stretched to make it 0.2%. What is the percentage change in its resistivity?
a. 0.4% b. 2.0% c. 4.0% d. none of these .

14. The resistance of a heating element is 99 at room temperature. What is the temperature of the
element, if the resistance is found to be 116 ? (Temperature coefficient of the material of the
resistor is 1.7×10−4 ⁰C−1)
a. 999.9 ⁰C b. 1005.3 ⁰C c. 1020.2 ⁰C d. 1037.1 ⁰C

15. A cell supplies a current of 0.9 A through a 2 resistor and a current of 0.3 A through 7
resistor. The internal resistance of the cell is:
a. 2.0 b. 1.5 c. 1.0 d. 0.5

16. A battery having 12 V emf and internal resistance 3 is connected to a resistor. If the current in
the circuit is 1 A, then the resistance of resistor and lost voltage of the battery when circuit is
closed will be:
a. 7 ,7V b. 8 ,8V c. 9 ,9V d. 9 , 10 V

17. Figure shows currents in a part of an electric circuit, then

current l is

a. 1.7 A b. 3.7 A
c. 1.3 A d. 1A

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18. In the circuit diagram, calculate the electric current through

branch BC

a. 4A b. 2A
c. 5A d. 10 A

19. In the given circuit the potential at point B is zero, the potential at points A and D will be

a. VA = 4V ; VD = 9V

b. VA= 3V ; VD= 4V

c. VA= 9V; VD = 3V d. VA= 4V; VD = 3V

20. Determine the electric current through branch BD of the electric

network

a. 0.6 A b. 0A
c. 1A d. 10 A

21. Four resistances of 3 , 3 , 3 and 4 respectively are used to a form of a Wheatstone bridge.
The 4 resistance is short circuited with a resistance R in order to get bridge balanced. The
value of R will be:
a. 10 b. 11 c. 12 d. 13

22. The resistances in left and right gap of a meter bridge are 20 and 30 respectively. When the
resistance in the left gap is reduced to half its value, the balance point shifts by:
a. 15 cm to the right. b. 15 cm to the left.
c. 20 cm to the right . d. 20 cm to the left.

23. In a meter bridge experiment, the ratio of the left gap resistance to right gap resistance is 2 : 3,
the balance point from left is:
a. 60 cm b. 50 cm c. 40 cm d. 20 cm

1. b 2. a 3. b 4. b 5. d
6. b 7. d 8. d 9. b. 10. a
11. c 12. c. 13 d. 14. d. 15. d
16. c 17. a 18 a 19. d 20. b
21. c 22. b 23. c

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