CURRENT

ELECTRICITY
What is electric current?
The constant flow of charge particles in a circuit is known as electric current. The
flow of electric current flows from higher potential to lower potential. Current is a
scaler quantity. It’s S.I. unit is Ampere (A). It’s formula is:- I=Q/T.

• Direction of current : The conventional direction of current is

taken to be the direction of flow of positive charge, i.e. field and is
opposite to the direction of flow of negative charge. Though
conventionally a direction is associated with current (Opposite to
the motion of electron), it is not a vector. It is because the current
can be added algebraically. Only scalar quantities can be added
algebraically not the vector quantities.
• Charge on a current carrying conductor : In conductor the current
is caused by electron (free electron). The no. of electron (negative
charge) and proton (positive charge) in a conductor is same.
Hence the net charge in a current carrying conductor is zero.
• Current through a conductor of non-uniform cross-section : For a
given conductor current does not change with change in cross-
sectional area. In the following figure i1 = i2 = i3.
Types Of Current:
There are two types of current:
1. Alternating Current (AC): In alternating current, the electric charge flow
changes its direction periodically. AC is the most commonly used and most-
preferred electric power for household equipment, office, buildings, etc. It was
first tested based on the principles of Michael Faraday in 1832 using a Dynamo
Electric Generator.
Alternating current can be identified in a waveform called a sine wave. In other
words, it can be referred to as a curved line. These curved lines represent electric
cycles and are measured per second. The measurement is read as Hertz (Hz). AC is
used in powerhouses and buildings because generating and transporting AC
across long distances is relatively easy. AC is capable of powering electric motors
which are used in refrigerators, washing machines, etc.
2. Directing Current(DC): Unlike alternating current, the flow of direct current
does not change periodically. The current electricity flows in a single direction
in a steady voltage. The major use of DC is to supply power to electrical
devices and also to charge batteries. Example: mobile phone batteries,
flashlights, flat-screen television and electric vehicles. DC has the combination
of a plus and a minus sign, a dotted line or a straight line.
Everything that runs on a battery and uses an AC adapter while plugging into a
wall or uses a USB cable for power relies on DC. Examples would be cellphones,
electric vehicles, flashlights, flat-screen TVs (AC goes into the TV and is converted
into DC).

Difference between AC and DC:

What is current density?
The amount of electric current traveling per unit cross-section area is called as
current density and expressed in amperes per square meter. The more the
current in a conductor, the higher will be the current density. However, the
current density alters in different parts of an electrical conductor and the effect
takes place with alternating currents at higher frequencies.

Electric current always creates a magnetic field. Stronger the current, the more
intense the magnetic field. Varying AC or DC creates an electromagnetic field and
this is the principle based on which signal propagation takes place.

Current density is a vector quantity having both a direction and a scalar

magnitude. The electric current flowing through a solid having units of charge per
unit time is calculated towards the direction perpendicular to the flow of
direction.

The formula for Current Density is given as,

J=I/A

Where,

I = current flowing through the conductor in Amperes

A = cross-sectional area in m2.

Current density is expressed in A/m2.

Potential applied across the end of the conductor is directly proportional to the
current flowing through a conductor, provided the physical conditions (such as
temperature) remain unchanged.’’
 V = IR or I = V/R,
where R is the constant of proportionality called resistance of the circuit
I in the current in amperes
V is the voltage across the conductor in volts.
From the above formula, it is clear that current is inversely proportional to
resistance. If resistance is doubled, the current is halved, and if the resistance is
halved, the current is doubled.

What is Electrical Resistance?

According to Ohm’s law, there is a relation between the current flowing through a
conductor and the potential difference across it. It is given by,
V I V = IR
Where,

V is the potential difference measured across the conductor (in volts)

I is the current through the conductor (in amperes)

R is the constant of proportionality called resistance (in ohms).

Rearranging the above relation,

R=VI
The unit of electrical resistance is ohms.
ohm=1 volt/1 ampere

Electric charge flows easily through some materials than others. The electrical
resistance measures how much the flow of this electric charge is restricted within
the circuit.

Factors Affecting Electrical Resistance:

The electrical resistance of a conductor is dependent on the following factors:

• The cross-sectional area of the conductor

• Length of the conductor
• The material of the conductor
• The temperature of the conducting material.
Electrical resistance is directly proportional to length (L) of the conductor and
inversely proportional to the cross-sectional area (A). It is given by the following
relation.
R=ρLA

where ρ is the resistivity of the material (measured in Ωm, ohm meter).

What is Resistivity?
Electric resistivity is defined as the electrical resistance offered per unit length
and unit cross-sectional area at a specific temperature and is denoted by
ρ. Electrical resistance is also known as specific electrical resistance. The SI unit of
electrical resistivity is Ωm. Following is the formula of electrical resistivity:
Ρ=E/J
Where,

• ρ is the resistivity of the material in Ω.m

• E is the electric field in V.m-1
• J is the current density in A.m-2
 Grouping of Resistance:
There are two types of combinations of Resistors:
1. Series Combination: Two or more resistors are said to be connected in
series when the same amount of current flows through all the resistors. In
such circuits, the voltage across each resistor is different. In a series
connection, if any resistor is broken or a fault occurs, then the entire circuit
is turned off. The construction of a series circuit is simpler compared to a
parallel circuit.

Resistors in series combination

For the above circuit, the total resistance is given as:
Rtotal = R1 + R2 + ….. + Rn
The total resistance of the system is just the total sum of individual resistances.
2. Parallel Combination: Two or more resistors are said to be connected in
parallel when the voltage is the same across all the resistors. In such
circuits, the current is branched out and recombined when branches meet
at a common point. A resistor or any other component can be connected or
disconnected easily without affecting other elements in a parallel circuit.

Resistors in parallel combination

The figure above shows the ‘n’ number of resistors connected in parallel. The
following relation gives the total resistance here
1 1 1 1
= + + ⋯.+
1 2
The sum of reciprocals of resistance of an individual resistor is the total reciprocal
resistance of the system.

Summary:
• A Circuit comprises conductors (wire), power source, load, resistor and
switch.
• Resistors control the flow of the electric current in a circuit.
• Two or more resistors are said to be connected in series when the same
amount of current flows through all the resistors.
• The following relation gives the total resistance of a series circuit:

Rtotal = R1 + R2 + ….. + Rn

• Two or more resistors are said to be connected in parallel when the voltage
is the same across all the resistors.
• The following relation gives the total resistance of a parallel circuit:
1 1 1 1
= + +⋯.+
1 2

• Sometimes, resistors in the same circuit can be connected in parallel and

series across different loops to produce a more complex resistive network.
These circuits are known as mixed resistor circuits.
Cell or Electrochemical Cell:
A cell or an electrochemical cell is a device that is capable of obtaining electrical
energy from chemical reactions or vice versa. You have definitely seen a cell, the
small AAA or AA batteries we use in our remotes.
An electric battery is a device made up of two or more cells that make use of the
chemical energy stored in the chemicals and converts it into electrical energy. A
battery is used to provide a continuous steady current source by way of providing
constant EMF or Electromotive force to an electrical circuit or a machine.

Each cell comprises two half-cells connected in series by a conductive electrolyte

containing anions and cations. One half-cell is made up of the electrolyte and the
negative electrode, the Anode. The negatively charged ions, also known as anions,
migrate to the Anode. The other half-cell includes the electrolyte and the positive
electrode, the Cathode, to which cations (positively charged ions) migrate.
Redox reactions, reduction and oxidation occur simultaneously and this powers
the battery. Cations are reduced (it gains electrons) at the cathode during
charging, while anions are oxidised (it loses electrons) at the anode during
charging. During discharge, the process is reversed. The electrodes do not touch
each other but are electrically connected by the electrolyte.
What is an Electromotive Force (EMF) of a cell?
When there is no electrical equipment attached to a cell i.e. no current is flowing
through the cell, the electrolyte has the same potential throughout the cell. The
condition of no current flowing through a cell is also known as an open circuit. In
an open circuit, the potential of the cell becomes equal to the difference in the
potentials of the electrodes. Anode has a positive potential (V +) whereas Cathode
has a negative potential (-V–). This potential difference is known as the
Electromotive Force (EMF) of the cell and it is equal to;
£= + − (− −) = + + −

We know that when we connect an appliance to the battery, a current flows

through the circuit that is proportional to the voltage. The ratio of the voltage (V)
across an object to the current flowing through it because of the potential is
known as the resistance of that object. Resistance in Electricity can be linked to
Friction in Mechanics. The electrical resistance of a body is the measure of the
difficulty in passing an electric current through it. The SI unit of electrical
resistance is ohm (Ω). The phenomenon of electrical resistance has led to the
creation of electrical heaters and induction cooktops. Resistance is given by

=
Internal Resistance:
Similar to how a body opposes the flow of electricity through it, leading to
resistance, the electrolytes in batteries have a finite value of resistance. The
resistance generated inside a battery to the flow of current is referred to as the
internal resistance of a battery (r). When a power source delivers current, the
measured voltage output is lower than the voltage when no current is flowing
through the circuit. This voltage drop is caused by the internal resistance of the
battery to the flow of current through it.
The voltage drop experienced due to internal resistance can be denoted as,
= + + − −
= £-
This internal resistance is usually neglected in real life since the electromotive
force (EMF) is quite larger than the internal resistance. When external electrical
equipment that uses current is attached to it, its own resistance (R) is also added
to this.
=
Substituting this into
= £-
= £-
£
=
+

What are Kirchhoff’s laws?

In 1845, a German physicist, Gustav Kirchhoff, developed a pair of laws that deal
with the conservation of current and energy within electrical circuits. These two
laws are commonly known as Kirchhoff’s Voltage and Current Law. These laws
help calculate the electrical resistance of a complex network or impedance in the
case of AC and the current flow in different network streams. In the next section,
let us look at what these laws state.

1. Kirchhoff’s First Law: This law is also known as junction rule or current
law (KCL). According to it the algebraic sum of currents meeting at a
junction is zero i.e. ∑i = 0.
In a circuit, at any junction the sum of the currents entering the junction must
equal the sum of the currents leaving the junction. i1+i3=i2+i4
Here it is worthy to note that :
(i) If a current comes out to be negative, actual direction of current
at the junction is opposite to that assumed, i+i2+i3= 0 can be
satisfied only if at least one current is negative, i.e. leaving the
junction.
(ii) This law is simply a statement of “conservation of charge” as if
current reaching a junction is not equal to the current leaving the
junction, charge will not be conserved.
 2. Kirchhoff’s Second Law: : This law is also known as loop rule or voltage
law (KVL) and according to it “the algebraic sum of the changes in potential
in complete traversal of a mesh (closed loop) is
zero”, i.e. ∑V = 0.
e.g. In the following closed loop.
– i1R1 + i2R2 – E1 – i3R3+ E2 + E3 – i4R4 = 0

Here it is worthy to note that :

(i) This law represents “conservation of energy” as if the sum of potential changes
around a closed loop is not zero, unlimited energy could be gained by repeatedly
carrying a charge around a loop.
(ii) If there are n meshes in a circuit, the number of independent equations in accordance
with loop rule will be (n – 1).

3. Sign convention for the application of Kirchoff’s law: For the application
of Kirchoff’s laws following sign convention are to be considered
(i) The change in potential in traversing a resistance in the direction of
current is – iR while in the opposite direction +iR.

(ii) The change in potential in traversing an emf source from negative to

positive terminal is +E while in the opposite direction – E irrespective of the
direction of current in the circuit.
 (ii) The change in potential in traversing a capacitor from the negative
terminal to the positive terminal is C q + while in opposite direction C q − .

(iv) The change in voltage in traversing an inductor in the direction of

current is –L di/dt while in opposite direction it is +L di/dt.

4. Guidelines to apply Kirchhoff’s Law:

(i) Starting from the positive terminal of the battery having highest emf,
distribute current at various junctions in the circuit in accordance with
‘junction rule’. It is not always easy to correctly guess the direction of
current, no problem if one assumes the wrong direction.
(ii) After assuming current in each branch, we pick a point and begin to
walk (mentally) around a closed loop. As we traverse each resistor,
capacitor, inductor or battery we must write down, the voltage change for
that element according to the above sign convention.
(iii) By applying KVL we get one equation but in order to solve the circuit we
require as many equations as there are unknowns. So we select the
required number of loops and apply Kirchhoff’s voltage law across each
such loop.
(iv) After solving the set of simultaneous equations, we obtain the
numerical values of the assumed currents. If any of these values come out
to be negative, it indicates that particular current is in the opposite
direction from the assumed one.
5. Determination of Equivalent resistance by Kirchhoff’s method: This
method is useful when we are not able to identify any two resistances in
series or in parallel. It is based on the two Kirchhoff’s laws. The method
may be described in the following guideline.
 (i) Assume an imaginary battery of emf E connected between the two
terminals across which we have to calculate the equivalent resistance.
(ii) Assume some value of current, say i, coming out of the battery and
distribute it among each branch by applying Kirchhoff’s current law.
(iii) Apply Kirchhoff’s voltage law to formulate as many equations as there
are unknowns. It should be noted that at least one of the equations must
include the assumed battery.
(iv) Solve the equations to determine i E ratio which is the equivalent
resistance of the network.
e.g. Suppose in the following network of 12 identical resistances, equivalent
resistance between point A and C is to be calculated.

According to the above guidelines we can solve this problem as follows

Step (1) Step (2)

Step (3) Applying KVL along the loop including the nodes A, B, C and the battery
E. Voltage equation is − 2iR−iR−iR− 2iR+ E = 0
Step (4) After solving the above equation, we get 6iR = E ⇒ equivalent resistance
between A and C is R=E/4i= 6iR/4i = 3/2R.
What is Drift Velocity?
Subatomic particles like electrons move in random directions all the time. When
electrons are subjected to an electric field they do move randomly, but they
slowly drift in one direction, in the direction of the electric field applied. The net
velocity at which these electrons drift is known as drift velocity.
Drift velocity can be defined as:

The average velocity attained by charged particles, (eg. electrons) in a material

due to an electric field.
The SI unit of drift velocity is m/s. It is also measured in m2/(V.s).

Average drift velocity and the direction of the electric field

Net velocity of electrons?

Every material above absolute zero temperature which can conduct like metals
will have some free electrons moving at random velocity. When a potential is
applied around a conductor the electrons will tend to move towards the positive
potential, but as they move, they will collide with atoms and will bounce back or
lose some of their kinetic energy. However, due to the electric field, the electrons
will accelerate back again, and these random collisions will keep happening but as
the acceleration is always in the same direction due to the electric field, the net
velocity of the electrons will also be in the same direction.

Formula to calculate Drift Velocity:

We can use the following formula in order to calculate drift velocity:
=
Where,

• I is the current flowing through the conductor which is measured in

amperes
• n is the number of electrons
• A is the area of the cross-section of the conductor which is measured in m2
• v is the drift velocity of the electrons
• Q is the charge of an electron which is measured in Coulombs
If the intensity of the electric field is increased then the electrons are accelerated
more rapidly towards the positive direction, opposite to the direction of the
electric field applied.

Relation between Drift Velocity and Electric

Current:
Mobility is always a positive quantity and depends on the nature of the charge
carrier, the drift velocity of an electron is very small usually in terms of 10-3ms-1.
Hence, at this velocity it will take approx. 17 mins for electrons to pass through a
conductor of 1 meter. But, surprisingly, we can turn on electronic appliances in
our home at lightning speeds with a flick of a switch this is because an electric
current is not established with the drift velocity but with the speed of light.

As soon as the electric field is established the current starts flowing inside the
conductor at the speed of light and not at the speed at which the electrons are
drifting, hence there is a negligible small delay between an input and an output in
turning on of an electric bulb.
What is Meter Bridge?
A Wheatstone bridge is a kind of electrical circuit used in measuring an electrical
resistance, which is unknown by balancing its two legs of the bridge circuit, where
one of the legs includes an unknown component. Samuel Hunter Christie created
this instrument in the year 1833 and was improved and also simplified by Sir
Charles Wheatstone in the year 1843. The digital multimeters in today’s world
provide the simplest forms in measuring the resistance. The Wheatstone Bridge
can still be used in measuring light values of resistances around the range of milli-
Ohms.

How is a Meter Bridge used in finding the Unknown

Resistance :
A meter bridge is an apparatus utilized in finding the unknown resistance of a coil.
The below figure is the diagram of a useful meter bridge instrument.
In the above figure, R is called as the Resistance, P is the Resistance coming across
AB, S is the Unknown Resistance, Q is the Resistance between the joints BD.
AC is the long wire measuring 1m in length and it is made of constantan or
manganin having a uniform area of the cross-section Such that L1 + L2 = 100
Assuming that L1 = L => L2 = 100 – L

Relation obtains the unknown resistance ‘X’ of the given wire:

X = RL2/L1 = R(100 – L)/L

And the specific resistance of the material for a given wire is obtained by the
relation = (3.14) r2X/l

where, r = the radius of the cable and also l = length of the wire.

The devices required in finding the unknown resistance of a conductor using a

meter bridge are:

• Meter bridge
• Resistance box
• Galvanometer
• Unknown Resistance of a length 1 m
• Screw gauge
• Connecting Wires
• Jockey
• One way key
In the meter bridge, one of the lateral kinds of resistances is replaced by a wire
having a length of the uniform cross section of about 1m. The other pair consists
of one known and an unknown pair of resistances. The one part of the
galvanometer is connected in between both resistances, whereas the other part
of the wire is finding the null point where the galvanometer is not showing any
deflection. At this point, the bridge is said to be balanced.

Procedure for finding the Unknown Resistance

using Meter Bridge:
 • Collect the instruments and prepare connections as shown in the above
figure.

• Take some suitable kind of resistance ‘R’ from the resistance box.

• Touch jockey at the point A; look that there exists a deflection in

galvanometer on one of the sides, then contact the jockey on point C of
wire, then the deflection in galvanometer has to be on another side.

• Find the position of the null point having deflection in the galvanometer
that becomes zero. Note the length AB (l) BC = (100 – l).

• Continue the above method for some different values of the ‘R’. Note at
least some 5 readings.

• Consider the point where galvanometer shows a 0 deflection; this is called

balance point.

• Now, Measure the length of given wire by the use of ordinary scale and
radius of the wire by the utilization of a screw gauge, (Take at least five
readings).

• Calculate Mean Resistance of Single Unknown Resistance = Total Sum of

resistances of Unknown resistance from the above five readings)/5.

What is a Potentiometer?
The potentiometer is basically a long piece of uniform wire across which a
standard cell is connected. In the actual design, the long wire is cut into several
pieces and it is placed side by side and connected at the ends with a thick metal
strip. The current flowing through the wire can be varied using a variable
resistance (rheostat) connected to the circuit. The resistance can be changed
manually for measuring the potential difference. The potential
difference between any two points in a circuit is the amount of work done in
bringing the charge from the first point to the second point. When there is a
potential difference there will be a current flow in the circuit.
The potentiometer is an instrument used for measuring the unknown voltage by
comparing it with the known voltage. It can be used to determine the emf and
internal resistance of the given cell and also used to compare the emf of different
cells. The comparative method is used by the potentiometer. The reading is more
accurate in a potentiometer.

Working principle of Potentiometer:

The basic principle of the potentiometer is that the potential drop across any
section of the wire will be directly proportional to the length of the wire, provided
the wire is of the uniform cross-sectional area and a uniform current flows
through the wire.

To determine the EMF of Cell:

Let us consider
that the potentiometer has a resistive wire of length ‘L’. Let one end of the wire
be A and the other end is taken as B. A battery is connected to the two ends of
the wire, this forms the primary circuit. The secondary circuit is formed by
connecting the end A of the wire to the cell whose emf has to be calculated and
the other terminal of the cell is connected to the galvanometer. The
galvanometer is further connected to the jockey (movable point). Let ‘i’ be the
current flowing through the wire.
i = ɛ/(r+R)
Here,
ɛ is the emf of the cell in the primary circuit
r is the internal resistance
R is the resistance of the wire
The voltage across the potentiometer wire of length L is taken as
VAB = V0
The fall of potential per unit length of the potentiometer wire is called the
potential gradient.
Z = (V0/L) is the potential gradient.
The jockey is moved on the wire and the null point (P) is determined. The point on
the wire is called the null point when the galvanometer will not show any
deflection. The length of the wire AP is taken as ‘l’.
The potential difference between A and P will be
c
( + )
− = .

⇒VA – VP = (V0/L).l
= Z.l = Ɛ’ (since V0 = iR)
Ɛ’ is the emf of the cell connected in the secondary circuit.

Comparison of two EMF of Cell:

The potentiometer can be used to compare the emf
of two cells of emf ε1 and ε2.
Let P1 be the null point when cell ε1 is connected and
let ‘l1’ be the length between the end A of the wire to
the null point P1. Then the potential difference
between A and P1 is
 VA – VP1 = Z.l1 = ε1 ———-(1)
Let P2 be the null point when the cell ε2 is connected and let ‘l2’ be the length
between the end A of the wire to the null point P2. Then the potential difference
between A and P2 is
VA – VP2 = Z.l2 = ε2 ————(2)
Comparing (1) and (2) we get
ε1 / ε2 = l1/l2
This simple mechanism thus allows one to compare the EMFs of any two sources.
In practice, one of the cells is chosen as a standard cell whose emf is known, then
the emf of the other cell can be easily calculated.

Measurement of Internal
Resistance of cell:
The potentiometer can also be used to measure
the internal resistance of the cell. To determine
the internal resistance, the cell whose internal
resistance has to be determined is connected
across the resistance box through the key(K1).
When the key is open the null point is obtained at
a distance l1 from A. Then,
ε = Z.l1 ——-(1)
When the key is closed a current ‘i’ is passed through the resistance box (R). Let
the null point be at a distance of l2 from A. Therefore, the potential difference will
be
v = Z.l2 ——–(2)
Comparing (1) and (2) we get
ε/v = l1/l2 ———(3)
We know ε = i(r+R) and v = iR
Therefore, equation (3) becomes
[i(r+R)/ iR] = l1/l2
Therefore, Internal resistance,
1
= ( − 1)
2

The potentiometer has the advantage that it draws no current from the voltage
source being measured. As such it is unaffected by the internal resistance of the
source.