Electric current is the flow of electric charge. It can be defined as the amount of charge passing through a cross-sectional area per unit time. Common types of current include steady direct current, varying direct current, and alternating current. Ohm's law states that the current through a conductor is directly proportional to the voltage applied. Resistance is a measure of how strongly a material opposes the flow of electric current. Kirchhoff's laws describe the conservation of electric charge and potential at nodes in a circuit.

1. G K GEORGE Page 1
CURRENT ELECTRICITY
Electric current: -
 It implies some sort of motion
 It denotes the motion of electric charge
 Electric current produced by motion of charge carriers in medium like
electrons in metal, ions in liquids and gases
 It is either due to flow of positive or negative charge
 Direction of current is taken as the direction of positive charge or
opposite to negative charge
 This will continue until the potential become equal
Electric current can be defined as amount of charge flowing through any cross
section of a substance in a unit time
Or
It is the rate of flow of charge through any cross section of a substance.
𝑰 =
𝑸
𝒕
If n carriers of electricity each having charge e, then
𝑰 =
𝒏𝒆
𝒕
Unit:- Ampere ( A )
The current through a wire is called one ampere, if one coulomb of charge
flows through the wire in one second.
Types of current: -
 Steady direct current
An electric current is said to be steady direct current if its magnitude
and direction do not change with time.

2. G K GEORGE Page 2
 Varying or variable direct current
An electric current is said to be varying direct current if its magnitude change
with time and polarity remains same
 Alternating current
An electric current is said to be alternating current if its magnitude changes
with time and polarity reverses periodically.
Current density: -
Current density of a conductor is defined as the amount of current flowing
per unit area of the conductor held perpendicular to the flow of current.
Current density= J = current / area, unit is A /m2
It is a vector quantity.
𝑑𝐼 = 𝐽
⃗ ∙ 𝑑𝑠
⃗⃗⃗⃗⃗
𝐼 = ∫ 𝐽
⃗∙ 𝑑𝑠
⃗⃗⃗⃗⃗
𝑠
Current is a scalar quantity

3. G K GEORGE Page 3
Current in a metallic conductor: -
 Free electrons are continuously moving about within the metal, with
different velocities in different directions
 During their travel, they collide with atoms (ions) gaining and losing
kinetic energy. Since motion is random, the average thermal velocity of
electrons is zero. As a result, there is no net flow of charge in any
direction.
When potential difference applied across the conductor, an electric field (𝑬
⃗⃗⃗)
established in the conductor. Due to this electric field, force experience on
electron opposite to the electric field (because electric field from positive to
negative). Due to this force, the electron acquired an acceleration
𝒆𝑬
𝒎
The acceleration will last only for short time, since electrons are deflected by
positive ions. Between successive collisions an electron acquired a velocity
component opposite to electric field.
If 𝝉 represents average time between successive collisions, the drift
velocity𝒗 =
𝒆𝑬
𝒎
𝝉
Or 𝒗
⃗
⃗⃗ =
−𝒆𝑬
⃗⃗⃗
𝒎
𝝉
The average additional velocity of free electrons in a conductor subjected to
an electric field is called Drift velocity.

4. G K GEORGE Page 4
RESISTANCE AND RESISTIVITY:
Ohm’s law:
The electric current I flowing through the substance is proportional to the
voltage across their ends.
V α I
V = RI
“When temperature is constant, the current flowing through a conductor is
directly proportional to the potential difference between the ends of the
conductor “
Resistance is the ratio of the potential difference applied across
the conductor to the current flowing through it.
R = V/I
Unit- ohm(Ω)
Dimension- ML2
T-3
A-2
Resistance of a conductor is said to be one ohm, if one ampere of current
flows through it, when a potential difference of one volt is applied across it.
Resistivity: -
At constant temperature, the resistance of the conductor is directly
proportional to the length and inversely proportional to the area of cross
section.

5. G K GEORGE Page 5
𝑅 α
𝑙
𝐴
, i.e. 𝑅 =
𝜌𝑙
𝐴
𝜌 =
𝑅𝐴
𝑙
If A= 1m2 and l=1m, then ρ = R
Resistivity of the material of a conductor is defined as the resistance of the
conductor of unit length and unit area of cross section.
Unit- ohm-metre ( Ω )
Dimension- ML3T-3A-2
The reciprocal of resistivity is called Conductivity
𝜎 =
1
𝜌
=
𝑙
𝑅𝐴
Color code: -
First two ------ significant figures
Third ----------- multiplayer
Forth ---------- tolerance
pq X 10r
±𝒔%
B B ROY Great Britain Very Good Wife

6. G K GEORGE Page 6
Origin of resistivity: -
Consider a conductor of length ’l’ and area of cross section A. Let n be the
electron density. When a voltage V is applied across its ends, a uniform electric
field E is established inside.
The magnitude of electric field 𝐸 =
𝑉
𝑙
If v be the drift velocity of electron, then the number of electrons
passing through the conductor per second is nAv
Therefore, the charge flowing through the conductor per second is nAve
I = nAve,V = IR
𝑬𝒍 = 𝒏𝑨𝒆𝒗𝑹
𝑬 =
𝒏𝒆𝒗𝑨𝑹
𝒍
= nev𝝆
But v = eEƮ / m

7. G K GEORGE Page 7
𝒗𝒎
𝝉𝒆
= 𝒏𝒆𝒗𝝆
or𝝆 =
𝒎
𝒏𝝉𝒆𝟐
ρ is related to n and collision time. The collision time depends on vibration of
atom of the metal. As temperature increases, the amplitude of vibration of the
atom increases. This lead to more collision of electrons with atom; thus
reducing the value of Ʈ, so the resistance of the conductor increases with
temperature.
Mobility: -
It is defined as the magnitude of the drift velocity per unit electric field.
𝜇 =
|𝑣𝑑|
𝐸
𝒗𝒅 =
𝒒𝑬
𝒎
𝝉
,
𝜇 =
𝑞𝝉
𝑚
Temperature dependence on resistivity: -
Resistivity increases with temperature since resistance is directly proportional
to resistivity.
Let R1 be the resistance at t1
0C and R2 at t2
0C (t2> t1)
The increase in resistance = R2 – R1
R2 – R1αR1
α(t2- t1)
i.e. R2 – R1αR1(t2- t1)
i.e. R2 – R1= 𝛼R1(t2- t1)
or α =
R2 – R1
R1(t2 − t1)
If t1 = 0 0
C and R1 =R0
t2 = t 0
C and R2 =R1

8. G K GEORGE Page 8
then, α =
𝑅1−𝑅0
𝑅0𝑡
α =
𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑎𝑡 00𝐶 𝑋 𝑟𝑖𝑠𝑒 𝑖𝑛 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒
The temperature coefficient of resistance is defined as the change in
resistance per unit original resistance per degree rise in temperature
Or
The ratio of increase in resistance for unit degree rise of temperature to
its resistance at 0 0C
 Resistance of the material generally increases with temperature. i.e.
they have positive temperature coefficient. Eg:-Aluminium, copper,
brass etc.
 Resistance of certain material does not vary with temperature. i.e. they
have zero temperature coefficient. Eg:- Manganin
 Resistance of certain material decreases with temperature. i.e. they
have negative temperature coefficient. Eg:- carbon, germanium and
silicon.
Limitations of Ohm’s law: -
 V depends on I non-linearly
This happens when the current through the conductor is very
large. The large current heats the conductor H = I2
Rt, thereby increases its
resistance and thereby decreases the current. i.e. voltage – current relation is
linear only for small currents
 The relation between V and I depend on the sign of V in addition to its
magnitude. When voltage V is applied across p-n junction, current
obtained only when the p-n junction is forward biased

9. G K GEORGE Page 9
 The relation between V and I is non-unique. This happens at low
temperature. It is found that at low temperature ( less than 4K), the
resistance of wire of length 2𝑙 𝑖𝑠 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 𝑡𝑤𝑖𝑐𝑒 𝑡ℎ𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 of
the same wire of length 𝑙
COMBINATION OF RESISTORS:
1) SERIES COMBINATION
In this case the current remains same and voltage different across
the resistors
V1 = IR1; V2 = IR2; V3 = IR3
IR = IR1 + IR2 + IR3
R = R1 + R2 + R3
2) PARALLEL COMBINATION

10. G K GEORGE Page 10
In this case the current different and voltage remains same across the
resistors
I = I1 + I2 + I3
𝑽
𝑹
=
𝑽
𝑹𝟏
+
𝑽
𝑹𝟐
+
𝑽
𝑹𝟑
𝟏
𝑹
=
𝟏
𝑹𝟏
+
𝟏
𝑹𝟐
+
𝟏
𝑹𝟑
EMF:-
It is defined as the potential difference between the terminals of a cell
in an open circuit.
In a conductor, the positive charge will flow in the direction of
electric field. To maintain a steady current, the conductor cannot be isolated, it
must be part of a closed circuit, that include an external device.
This device is required to transport positive charge from low
potential to high potential, thus maintain a potential difference between the
two points. The external device will need to do work for it. Such a device is the
source of EMF.
The work done by the cell in forcing unit positive charge to flow in the whole
circuit (includingcell) is called the emf of the cell.
Terminal potential difference: -
Terminal potential difference of a cell is defined as the potential
difference between its terminals in a closed circuit.
Internal resistance: -
It is defined as the opposition offered by a cell to the flow of current through
it. It is denoted by r. It depends on nature of the electrolyte and electrodes.
Relation between EMF and Terminal potential Difference: -

11. G K GEORGE Page 11
When K is closed, 𝐼 =
𝐸
𝑅+𝑟
𝐸 = 𝐼𝑅 + 𝐼𝑟
Since R is parallel to electrodes of the cell, so the terminal potential difference
of the cell is equal to the potential difference across R
i.e. V = IR
Therefore, 𝐸 = 𝑉 + 𝐼𝑟
i.e Terminal potential difference is less than EMF ( TPD will be more than EMF
when the battery is charging)
Internal Resistance: -
𝐼 =
𝐸
𝑅 + 𝑟
𝑉 =
𝐸𝑅
𝑅+𝑟
, 𝑅 + 𝑟 =
𝐸𝑅
𝑉
Or 𝑟 = [
𝐸
𝑉
− 1] 𝑅
Grouping of cells:-
1) Series grouping:
Consider n identical cells, each of emf E and internal resistance r connected in
series to an external resistance R

12. G K GEORGE Page 12
Eeff = E + E + E + E + ……….. = nE
reff = r + r + r + …………….. = nr
Total resistance = R + nr
Current I = effective emf / equivalent resistance
I = nE / ( R + nr )
Special case:-
i) R >> nr
I = n ( E/R)
In order to get a large amount of current from the cells connected in series; the
external resistance will be very large as compared to effective internal
resistance.
ii) R<<nr; I= E/r is the current due to single cell.
2) Parallel grouping: -
Consider m identical cells each of emf E and internal resistance r.

13. G K GEORGE Page 13
Total emf = E
1/reff = 1/r + 1/r +………………..= m/r
Therefore I = E / (R + r/m) = mE/ (mR + r)
Special case:-
i) If R>>r; R+r/m =R
I = E/R, current due to single cell.
ii) If R<<r; R+r/m =r/m, then I = mE/r.
In order to get large current, the cells may be connected in parallel to
a small external resistance.
Mixed grouping of cells:
Eeff = nE
1/reff = 1/nr + 1/nr + ………………=m/nr
𝑰 =
𝒏𝑬
𝑹 +
𝒏𝒓
𝒎
=
𝒏𝒎𝑬
𝒎𝑹 + 𝒏𝒓
The current in the circuit will be maximum if mR + nr = minimum
𝒎𝑹 + 𝒏𝒓 = {√𝒏𝒓 − √𝒎𝑹}
𝟐
+ 𝟐√𝒎𝒏𝒓𝑹
mR + nr = minimum means the quantity √nr − √mR is minimum. It is a
square term, so never be negative. So the least possible value is zero.
√𝒏𝒓 = √𝒎𝑹
i.e. nr = mR or R = nr/m

14. G K GEORGE Page 14
Thus, in order to get the maximum current in the circuit, the mixed grouping of
cells must be done in such a way that the external resistance is equal to the
effective internal resistance of the cells.
KIRCHHOFF’S LAWS: -
1) Current law or junction law
It states that the sum of all the currents entering in any point (junction) must
be equal to the sum of all the currents leaving that point (junction).
Or
The algebraic sum of all the currents meeting at a point (junction) in a closed
electrical circuit is zero.
I1 + I2- I3- I4- I5=0
The current entering to the point is taken as positive and while current
leaving the point is taken as negative.
2) Voltage law or Loop law: -
It states that the algebraic sum of the products of the currents and
resistances of any closed loop is equal to the total emf in that loop.
∑ 𝑰𝑹 = ∑ 𝑬

15. G K GEORGE Page 15
In loop ABCFA, I1R1-I2R2 = E1-E2
In loop CDEFC, I2R2 +( I1+I2)R3 = E2
In loop ABCDEFA, I1R1+(I1+I2)R3 = E1
WHEATSTONE BRIDGE:-
It is an arrangement of 4 resistances used for measuring one unknown
resistance in terms of the other 3 known resistances
Principle:-
When key KG is closed, galvanometer G shows deflection, i.e. the presence of
Ig. The value of R is adjusted in such a way that galvanometer shows no
deflection. At this stage the potential at points B and D are equal. The
wheatstone bridge is balanced at this stage.Then,
𝑃
𝑄
=
𝑅
𝑆
OR 𝑆 = (
𝑄
𝑃
) 𝑅
Proof:-
At the junction A, the current I divide into I1 through P and ( I-I1) through R.
Applying Kirchhoff’s law to the loop ABDA
I1P + IgRg - ( I - I1 )R = 0
I1P + IgRg = ( I - I1 )R------------------------(1)
For the loop BCDB

16. G K GEORGE Page 16
( I1-Ig)Q - ( I - I1 + Ig)S -IgRg= 0
( I1-Ig)Q = ( I - I1 + Ig)S+IgRg------------------------(2)
When bridge is balanced, Ig = 0.
So (1) and (2) becomes
I1P = ( I - I1 )R------------------------(3)
I1Q = ( I - I1 )S------------------------(4)
(3)/(4),
𝑃
𝑄
=
𝑅
𝑆
Metre bridge:-
It consists of one metre resistance wire. The ends of the wire
connected to two thick copper strips. A third copper strip is placed between
the above, providing two gaps G1 and G2. The resistance box is connected at
G1 and the resistance to be measured is connected to G2.
Close the key and adjust the known value of resistance R from the
resistance box. Now move jokey(J) over the wire AC so that the galvanometer
shows no deflection. Now the bridge is said to be balanced.
Let the resistance between A and B = P
the resistance between B and C = Q
If r be the resistance per unit length, then
𝑃 = 𝑟𝑙, 𝑎𝑛𝑑 𝑄 = (100 − 𝑙)𝑟
𝑺 = (
𝑸
𝑷
) 𝑹 =
(𝟏𝟎𝟎 − 𝒍)𝒓𝑹
𝒍𝒓
=
(𝟏𝟎𝟎 − 𝒍)𝑹
𝒍
Potentiometer: -

17. G K GEORGE Page 17
Principle:
When a constant current is passed through a wire of uniform area of cross
section; the potential drop across any portion of the wire is directly
proportional to the length of that portion.
 It consists of a uniform resistance wire
 There is a jokey which can be moved along the wire to make any contact
with it at any point
 A cell of emf E connects in series with potentiometer wire forms the
primary circuit
Let V be the potential difference across any portion of length 𝒍,
resistance R and uniform area of cross section A. if 𝑰 be the current flowing
through the wire.
V = IR =
𝑰𝝆𝒍
𝑨
= [
𝑰𝝆
𝑨
] 𝒍 = 𝒌𝒍
i.e. V α𝒍, provided I,ρ and A are constants.
Comparison of emf’s of 2 cells: -
The positive terminal of the cell is connected to A and the negative
terminal is connected to B through rheostat and key. The cells whose emfs to
be compared are connected by using keys a and b. The key a is adjusted in such
a way that E1 is included in the circuit. Balancing length is measured as 𝒍𝟏 by
null deflection method. Then key b is adjusted for E2. So balancing length is 𝒍𝟐.

18. G K GEORGE Page 18
𝑬𝟏 ∝ 𝒍𝟏 ; 𝑬𝟐 ∝ 𝒍𝟐
𝑬𝟏 = 𝒌𝒍𝟏; 𝑬𝟐 = 𝒌𝒍𝟐
𝑬𝟏
𝑬𝟐
=
𝒍𝟏
𝒍𝟐
Determination of internal resistance of a cell by using Potentiometer: -
Step-1
K1 is closed and K2 is open. At the point S, jokey give null deflection.
𝑬 ∝ 𝒍𝟏; 𝑬 = 𝒌𝒍𝟏
Step-2
K2 is closed so that the known resistance is connected across the cell.
Find the null deflection. The terminal potential difference 𝑽 ∝ 𝒍𝟐
𝑽 = 𝒌𝒍𝟐
𝑬
𝑽
=
𝒍𝟏
𝒍𝟐
Internal resistance, 𝑟 = [
𝐸
𝑉
− 1] 𝑅
𝑟 = [
𝑙1
𝑙2
− 1] 𝑅
*notes printed in red colour excluded from the syllabus for the academic
session 2023-24