CURRENT ELECTRICITY

1. Electric Current
2. Conventional Current
3. Drift Velocity of electrons and current
4. Current Density
5. Ohm‘s Law
6. Resistance, Resistivity, Conductance &
Conductivity
7. Temperature dependence of resistance
8. Colour Codes for Carbon Resistors
9. Series and Parallel combination of
resistors
10. EMF and Potential Difference of a cell
11. Internal Resistance of a cell
12. Series and Parallel combination of cells

Created by: SONWANE SACHIN SHASHIKANT, K V No.1, KPA, KOLKATA

13. Kirchhoff‘s Laws of electricity
14. Wheatstone Bridge
15. Metre Bridge
16. Potentiometer
i) Principle
ii) Comparison of emf of primary cells
Electric Current:
The electric current is defined as the charge flowing through
any section of the conductor in one second.
The branch of Physics, which deals with the study of charges in
motion is called Current electricity.
SI unit: ampere (A)

I b c
Different types of current: a

a) Steady current which does not

vary with time
d
b) & c) Varying current whose 0
magnitude varies with time t

d) Alternating current whose

magnitude varies continuously
and direction changes
periodically
ELECTROMOTIVE FORCE :
Electric current is possible in a closed circuit if there is a source of
external force which compels the current carriers to move in a definite
direction.
This external force which makes the current to move in a definite
direction is called electromotive force (emf).
E.M.F. of a cell is defined as the maximum potential difference between
the two electrodes of the cell when no current is drawn from the cell or
cell is in the open circuit.

SI unit of emf of a cell : volt (V) or joule per coulomb (J/C)

Conventional Current:
Conventional current is the current + -
+ + + + -
whose direction is along the direction of
the motion of positive charge under the + -
+ I -
action of electric field.
Conventional current due to motion of -
- - - +
electrons is in the direction opposite to -
+
that of motion of electrons. -
+
- I
+

Electric current will mean only the conventional current which flows from
positive end (higher pot.) to negative end (lower pot.) in the closed circuit.

Current is a scalar quantity.

The electric current represented the direction of flow of positive charge,
yet it is treated as a scalar quantity because current follows the laws of
scalars addition and not the laws of vectors addition.
Drift Velocity :
Drift velocity is defined as the average l
velocity with which the free electrons get
drifted towards the positive terminal A vd - - -E
under the effect of the applied external
electric field. I

At room temperature, electrons move at random within the body of the

conductor
The av. thermal speed of free electron at room temp. is 105 ms-1

Average thermal velocity of electrons is zero (due to random distribution)

P.D. applied between two ends of conductor—field is set up inside—free

electron experience a force in opposite direction of field—e- accelerated
from –ve terminal to +ve terminal—suffer frequent collision—lose K.E.—
process repeats and continues till the electron reach the +ve terminal.
The drift velocity of electron is of the order of 10-4 ms-1

Similarly, the velocities acquired by other electrons in the conductor will be

 Average relaxation time = mean free path of electron or drift speed of electron

MOBILITY :
Mobility of charge carrier is defined as the magnitude of drift velocity of
charge per unit electric field applied.

SI unit : m2s-1V-1
RELATION BETWEEN CURRENT AND DRIFT VELOCITY :
Consider a conductor of length l and uniform area of cross-section A.
l
Let n is the number density of electrons. (nAl)
If e is the chare on each electron, then A vd - - -E
total charge on all the free electron is
I
Let a constant P.D. V be applied with the
help of battery.
The electric field E is set up across the conductor.

Time taken by the free electron to cross the conductor is

Ohm‘s Law:
The electric current (I) flowing through a conductor is directly
proportional to the potential difference (V) across the two ends of the
conductor when physical conditions such as temperature, mechanical
strain, etc. remain the same.

I I

0
V V
IαV or V α I or V = R I

where R is known as resistance of the conductor.

It depends upon the length, shape and the nature of material of the
conductor. It also depends on temp. of the conductor.
Deduction of Ohm‘s law:

We know that,

ELECTRICAL RESISTANCE :
The resistance of conductor is the opposition offered by the conductor
to the flow of electric current through it.
It is also defined as the ratio of the potential difference (V) applied
across the ends of the conductor to the current (I) flowing through it.

Symbol :
Specific Resistance or Resistivity :
The resistance of a conductor depends upon
i) Length iii) Nature of material
ii) Area iv) Temperature of the conductor

Practically, Resistance is directly proportional to length of the conductor

and inversely proportional to area of cross section.

where ρ is constant of proportionality and known as specific

resistance or resistivity.
If l=1, A=1, then R = ρ
Unit of resistivity:
Factors affecting Specific resistance :

comparing above equations we get

τ depends upon temp. of the conductor, so resistivity of conductor changes with temp.

T ρ
Current density:
Current density at a point, within a conductor, is the current through a unit
area of the conductor, around that point, provided the area is perpendicular
to the direction of flow of current at that point.

SI unit : Am-2

In vector form, I = J . A

Conductance and conductivity:

Conductance is the reciprocal of resistance. SI unit : mho

Conductivity is the reciprocal of resistivity. SI unit : mho / m or S/m

Relation between resistivity and mobility :
Temperature dependence of Resistances:
When temperature increases, the no. of collisions
increases due to more internal energy and relaxation time
decreases. Therefore, Resistance increases.
The resistance Rt of a metal conductor at temp. t 0C is given as

Thus, temp. coefficient of resistance (α) is defined as the increase in

resistance per unit original resistance per degree celsius or kelvin rise of
temperature.

R0 – Resistance at 0°C
Rt – Resistance at t°C
R2 – R1 R1 – Resistance at t1°C
or α =
R1t2 – R2t1 R2 – Resistance at t2°C

If R2 < R1, then α is – ve.

Colour code for carbon resistors:
The first two rings from the end give the
first two significant figures of B V B Gold
resistance in ohm. 17 x 100 = 17 ± 5% Ω
The third ring indicates the decimal
multiplier.
The last ring indicates the tolerance in
per cent about the indicated value. G R B Silver
Eg. AB x 10C ± D % ohm 52 x 106 ± 10% Ω

BVB
17 x 100 = 17 ± 20% Ω

B B ROY of Great Britain has Very

Good Wife
Another Colour code for carbon resistors:
i) The colour of the body gives the first
significant figure. Red Ends Yellow Body Gold Ring
ii) The colour of the ends gives the second
Blue Dot
significant figure.
iii) The colour of the dot gives the decimal YRB Gold
multipier.
42 x 106 ± 5% Ω
iv) The colour of the ring gives the
tolerance.
Series combination of resistors:
Resistors are said to be connected in series, if the same current is
flowing through each resistor when some potential difference is
applied across the combination.
If the three resistances R1, R2, R3
A B
R1 R2 R3 are connected end to end.
I Let V be the potential difference
applied across A and B using the
battery.
V
In series combination, the same current will be passing through each resistor.
Let V1, V2, V3 be the potential differences across R1, R2 and R3 respectively.
According to Ohm‘s law A B
RS
V1=IR1, V2=IR2, V3=IR3 I
V = V1+ V2+ V3 = IR1 + IR2 + IR3
= I (R1 + R2 +R3) V
IRS = I (R1 + R2 + R3) If RS is the equivalent resistance of the given
series combination of resistances, then
RS = R1 + R2 + R3
V = IRS

RS is greater than the greatest of all.

Parallel combination of resistors:
Any number of resistors are said to be connected in parallel if potential
difference across each of them is the same and is equal to the applied
potential difference.
R1

R2 Potential difference across each resistor is V

R3

If RP is the equivalent resistance of the given

RP
I parallel combination of resistance then
or

RP is smaller than the smallest of all.

Sources of emf:

The electro motive force is the maximum potential difference between the
two electrodes of the cell when no current is drawn from the cell.

Comparison of EMF and P.D:

EMF Potential Difference
1 EMF is the maximum potential P.D is the difference of potentials
difference between the two between any two points in a closed
electrodes of the cell when no circuit.
current is drawn from the cell
i.e. when the circuit is open.
2 It is independent of the It is proportional to the resistance
resistance of the circuit. between the given points.

3 The term ‗emf‘ is used only for It is measured between any two
the source of emf. points of the circuit.

4 It is greater than the potential However, p.d. is greater than emf

difference between any two when the cell is being charged.
points in a circuit.
INTERNAL RESISTANCE OF A CELL:
The opposition offered by the electrolyte and electrodes of a cell to the
flow of electric current through it (cell).
Factors affecting Internal Resistance of a cell:
i) Larger the separation between the electrodes of the cell, more the length
of the electrolyte through which current has to flow and consequently a
higher value of internal resistance.
ii) Greater the conductivity of the electrolyte, lesser is the internal resistance
of the cell. i.e. internal resistance depends on the nature of the electrolyte.
iii) The internal resistance of a cell is inversely proportional to the common
area of the electrodes dipping in the electrolyte.
iv) The internal resistance of a cell depends on the nature of the electrodes.

E =V+v E r
= IR + Ir v
I I
= I (R + r)
R
I = E / (R + r)
This relation is called circuit equation. V
Internal Resistance of a cell in terms of E,V and R:

E =V+v E r
= V + Ir
Ir = E - V v
I I
Dividing by IR = V, R

Ir E–V E V
= r =( - 1) R
IR V V

Determination of Internal Resistance of a cell by voltmeter method:

V V
+ +

r r

I I
R.B (R) R.B (R)
K K
Open circuit (No current is drawn) Closed circuit (Current is drawn)
EMF (E) is measured Potential Difference (V) is measured
Grouping of two un-identical cells :
1] Series Combination -
The two cells are connected in series, when negative terminal of one cell
is connected to positive terminal of other cell.

P Q I R
Let E1 and E2 be the emfs of the two cells and r1 and r2 be their internal
resistances respectively.
Let VP, VQ and VR be the potentials at point P, Q and R, and the I
current flowing through them

P.D. between P and R of series If the series combination of two cells is

combination of the two cells is replaced by a single cell between P and R of
emf Eeq and internal resistance req then

For n cells

Comparing eq. (i) and (ii)

Case : If negative terminal of first cell is connected to the negative terminal
of the second cell between points P and R then

P Q I R
Grouping of number of identical cells:
1] Series grouping of cell -
Cells are connected in series when they are joined end to end so that the
same quantity of electricity must flow through each cell.
NOTE: E r E r E r
1. The emf of the battery is the
sum of the individual emfs I I
2. The current in each cell is the R
same and is identical with the
current in the entire
V
arrangement.
3. The total internal resistance of
the battery is the sum of the
individual internal resistances.
Total emf of the battery = nE (for n no. of identical cells)
Total Internal resistance of the battery = nr
Total resistance of the circuit = nr + R
nE
Current I = (i) If R << nr, then I = E / r (ii) If nr << R, then I = n (E / R)
nr + R

Conclusion: When internal resistance is negligible in comparison to the external

resistance, then the cells are connected in series to get maximum current.
2] Parallel grouping of cells -
Cells are said to be connected in parallel when they are joined positive to
positive and negative to negative such that current is divided between the
cells.
E r
NOTE:
1. The emf of the battery is the same as that of a
single cell. E r
2. The current in the external circuit is divided equally
among the cells.
3. The reciprocal of the total internal resistance is the I E r
sum of the reciprocals of the individual internal I
resistances.
Total emf of the battery = E R

Total Internal resistance of the battery = r / m V

Total resistance of the circuit = (r / m) + R

mE
Current I = (i) If R << r/m, then I = mE / r (ii) If r/n << R, then I = E / R
mR + r

Conclusion: When external resistance is negligible in comparison to the internal

resistance, then the cells are connected in parallel to get maximum current.
3] Mixed grouping of cells -

E r E r E r

E r E r E r

E r E r E r
I I

V
In each row there are n cells in series,
The current in the external
resistance R is,
There are m rows of cells in parallel
Heat produced by electric circuit :
A B
Consider a conductor AB of resistance R. R
I
Let V be the P.D. applied across it (AB)
I be the current flowing through AB in time t.

By definition of P.D. ,
work done in carrying unit charge from A to B is

This work done is called electric work done. This work done appears as heat.
Then amount of heat produced (H) is given by

―Whenever an electric current is passed through a conductor, it becomes hot

after some time. This effect is known as heating effect of current (Joule
heating effect).‖
Eqn. (iii) is known as Joule‘s law of heating.
Thus, Joule‘s law of heating states that the amount of heat produced in a
conductor is directly proportional to square of current flowing through the
conductor, resistance of the conductor and time for which the current is
passed.
Electric Power :
The rate at which electric work is done by the source of emf in maintaining
the current in electric circuit is called electric power of the circuit.

1 watt = 1 volt X 1 ampere

Commercial unit of power is horse power (hp), 1 hp = 746 watt
Efficiency of an electric device (η) :
Efficiency of an electric device is defined as the ratio of its output power
to the input power.

Electric energy :
The total electric work done or energy supplied by the source of emf in
maintaining the current in an electric circuit for a given time is called
electric energy consumed in the circuit.
Electric energy = electric power x time
Commercial unit of electric energy is kilowatt-hour (kWh)
1 kWh = 1 kilo-watt x 1 hour 1 kWh = 3.6 x 106 J
KIRCHHOFF‘S LAWS:
I Law / Current Law / Junction Rule:-
The algebraic sum of electric currents at a junction in any electrical
network is always zero.

I1 I5

I3 I1 + I2 - I3 - I4 - I5 = 0
O
I2
I4

Sign Conventions:
1. The incoming currents towards the junction are taken positive.
2. The outgoing currents away from the junction are taken negative.

Note: The charges cannot accumulate at a junction. The number

of charges that arrive at a junction in a given time must leave in
the same time in accordance with conservation of charges.
II Law / Voltage Law / Loop Rule:
The algebraic sum of all the potential drops and emf‘s along any
closed path in an electrical network is always zero.
I1 E1 R1 I1
A B Loop ABCA:

R2 - E1 + I1.R1 + (I1 + I2).R2 = 0

I2 I 1 + I2 I1
Loop ACDA:
D C
I2 R3 I2 - (I1 + I2).R2 - I2.R3 + E2 = 0
E2
Sign Conventions:
1. The emf is taken negative when we traverse from positive to negative
terminal of the cell through the electrolyte.
2. The emf is taken positive when we traverse from negative to positive
terminal of the cell through the electrolyte.
3. The potential fall is taken negative.
4. The potential rise is taken positive.
The potential falls along the direction of current in a current path and it
rises along the direction opposite to the current path.
Note: The path can be traversed in clockwise or anticlockwise direction of
the loop.
 B
Wheatstone Bridge Principle:
P Q
Wheatstone bridge is an arrangement of
four resistances in the form of a bridge I1 I1 - Ig
Ig
which is used for measuring one
unknown resistance in term of other
A G C
three known resistances.
P R
R S
Q S
I - I1
Currents through the arms are assumed by I I - I1 + Ig I
applying Kirchhoff‘s Junction Rule. D
Applying Kirchhoff‘s Loop Rule for:
Loop ABDA, -I1P - IgG + (I - I1)R = 0----(i)
I E I
Loop BCDB, - (I1 - Ig)Q + (I - I1 + Ig)S + IgG = 0 ----(ii)

When Ig = 0, the bridge is said to balanced. Then eq. (i) and (ii) can be
written as
I1P = (I - I1)R ----(iii) P R
Dividing (iii) by (iv), we get
I1Q = (I - I1)S ----(iv) Q S
Meter Bridge (Slide wire bridge) :-
R.B (R) X
A meter bridge is a practical
form of Wheatstone bridge D

Meter Bridge is based

G
on the principle of
Wheatstone Bridge.
A J C
When the galvanometer
l cm B 100 - l cm
current is made zero by
adjusting the jockey
position on the meter- K
bridge wire for the given E
values of known and
unknown resistances,

R lσ R l (Since, σ is the
resistance per cm
X (100-l)σ X 100 - l length of the wire.)
POTENTIOMETER AND ITS PRINCIPLE OF WORKING :
Potentiometer is an apparatus used for measuring potential difference
between two points in an electrical circuit accurately.
It is also used for comparing the emf‘s of two cells and for measuring
internal resistance of a cell.
It consists of a long uniform wire ( manganin / constantan) stretched on a
wooden board.
Four or more wires, each one metre long, fixed parallel to one another and
connected in series (thick copper strips)
A metre scale is fixed on the board parallel to the length of the wire.
Its ends are connected to the binding screws A and B.
+
The potentiometer is provided
V with a jockey J with the help of
E A
0 l cm J 100
which, the contact can be made
at any point on the wire.
A 200
+ 300 A battery E, an ammeter A, a
Rh B key K and a rheostat Rh are
400
connected in series with
potentiometer wire.
K
Principle :
Suppose A is the area of cross section and ρ is specific resistance of the
material of the wire.
Let V be the potential difference across the portion of the wire of length l
whose resistance is R.
If I is the current flowing through the wire, then
V = IR
= I ρl/A
V = Kl
or V α l
The potential difference across any length of a wire of uniform cross-
section and uniform composition is proportional to its length when a
constant current flows through it.

0
l
DETERMINATION OF POTENTIAL DIFFERENCE USING POTENTIOMETER :
A battery of emf E is connected to end terminals A and B of
potentiometer wire with ammeter, resistance box R and key K in series.
(Auxiliary circuit)
The ends of resistance R1 are connected to terminal A and jockey J
through galvanometer G.
A cell E1 and key K1 are connected across R1
E1 K1
Close the key K.
G
Take out suitable resistance
R1 R from resistance box.
E A
0 l cm J Close the key K1
100
A 200 The current flows through R1.
+ P.D. is developed across R1.
300
R B Adjust the position of jockey
400 on potentiometer wire (G
shows no deflection)
K Let it be when jockey is at J.

Note the length AJ (AJ=l )

When potential difference across R1 is equal to the fall of potential across the
potentiometer wire of length l.
If K is the potential gradient of potentiometer wire, then P.D. across R1 is

If r is the resistance of potentiometer wire of length L, then current theough

potentiometer wire is,

Potential gradient of potentiometer wire is,

From eq.n (i) and (ii)

Comparison of emf‘s using Potentiometer: E1
R.B
The balance point is obtained I + G
for the cell when the potential +
at a point on the potentiometer E2
E A
wire is equal and opposite to 0 l2 J2 100
the emf of the cell.
A 200 l1 J1
+
300
Rh
E1 = VAJ1 = I ρl1 /A B 400

E2 = VAJ2 = I ρl2 /A
K
E1 / E2 = l1 /l2
Note:
The balance point will not be obtained on the potentiometer wire if the fall
of potential along the potentiometer wire is less than the emf of the cell to
be measured.
The working of the potentiometer is based on null deflection method. So
the resistance of the wire becomes infinite. Thus potentiometer can be
regarded as an ideal voltmeter.
Internal Resistance of a cell by Potentiometer :
To find the internal resistance r of a cell of emf E using potentiometer, set
up the circuit as shown. E‘
Close the key K and maintain I + G
suitable constant current in the
potentiometer wire with the help R.B
R K1
of rheostat. E A 100
0 l2 J2
Adjust the position of jockey on 200
the potentiometer wire where if A l1 J1
+ 300
pressed the galvanometer
shows no deflection . Rh B 400
Let it be when jockey is at J1.
(AJ1=l1)
K
Emf of the cell E‘ = P.D. across the length l1 of the potentiometer wire.
As no current is being drawn from the cell, E‘ =Kl1
Take out suitable resistance R from the resistance box in the cell circuit
and close key K1.
Again find the position of jockey on the potentiometer wire where
galvanometer shows no deflection.
Let it be at J2. (AJ2=l2)
As current is being drawn from the cell, its terminal potential difference V
and not the emf E‘ is balanced across AJ2.
Therefore, P.D. between two terminals of the cell. V across the length l2 of
the potentiometer wire, V=Kl2
𝑬′ 𝒍𝟏
∴ =
𝑽 𝒍𝟐
Internal resistance r of a cell of emf E‘, when a resistance R is connected
in its circuit is given by,
V = E‘- Ir
Ir = E‘- V
𝑬′ − 𝑽 𝑬′ − 𝑽 𝑬′ − 𝑽
𝒓= = = ×𝑹
𝑰 𝑽 𝑽
𝑹
𝑬′
𝒓= −𝟏 ×𝑹
𝑽
𝒍𝟏
𝒓= −𝟏 ×𝑹
𝒍𝟐
Sensitivity of Potentiometer:
The sensitivity of potentiometer means the smallest P.D. that can be
measured with its help.
Sensitivity of a potentiometer can be increased by decreasing its potential
gradient.
It can be achieved by
(i) increasing the length of potentiometer wire
(ii) reducing the current in the potentiometer wire circuit by
increasing the resistance with the help of rheostat.
Difference between Potentiometer and Voltmeter:

Potentiometer Voltmeter

1. It measures the emf of a cell very 1. It measures the emf of a cell

accurately. approximately.
2. It is based on null deflection method. 2. It is based on deflection method.

3. It can be used for various purposes. 3. It can be used only measure emf or
P.D.
4. Its sensitivity is high. 4. Its sensitivity is low.

5. Resistance of potentiometer 5. Resistance of voltmeter is high but

becomes infinite. finite.
6. Does not draws current from the 6. Draws some current from the
source. source.