CBSE Class 12 Physics Revision Notes Chapter 3: Current Electricity

Current electricity is the continuous flow of electric charge through a conductor under an applied potential difference. In CBSE Class 12 Physics, it connects electron drift, resistance, electrical power, cells and circuit laws.

Current Electricity explains how electric charges move through conductors. The chapter develops the relation between current, drift velocity, resistance and the electric field. It also covers cells, electrical power and circuit analysis.

Use these CBSE Class 12 Physics Revision Notes Chapter 3 for the 2026–27 session. Revise definitions and microscopic relations first. Then study resistor combinations, cells, Kirchhoff’s rules and the Wheatstone bridge.

Key Takeaways

• Electric current: I = dQ/dt measures charge crossing a section per unit time.
• Drift relation: I = neAvd connects current with free-electron motion.
• Ohm’s law: V = IR applies when resistance remains constant.
• Cell current: I = ε/(R + r), where r is the internal resistance.

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Electric Current and Current Density Class 12 Physics Notes

Electric current appears when charges have a net directed motion. In metallic conductors, free electrons carry current through a background of fixed positive ions.

Electric Current

Electric current is the rate at which net charge passes through a cross-section of a conductor.

For steady current:

I = Q/t

For a current that changes with time:

I = dQ/dt

Here:

• I is electric current.
• Q is the net charge.
• t is time.

The SI unit of current is ampere.

1 A = 1 C/s

Electric current is a scalar quantity. Its direction is represented by an arrow for circuit convenience.

Direction of Conventional Current

Conventional current flows in the direction of positive charge motion.

In a metallic conductor:

• Electric field acts from higher potential to lower potential.
• Conventional current follows the electric field.
• Electrons drift opposite to the electric field.
• Electrons move from lower potential to higher potential.

The direction of current is therefore opposite to the direction of electron drift.

Current Density

Current density is the current flowing normally through unit cross-sectional area.

For uniform current flow:

j = I/A

In vector form:

I = j·A

Here, A represents the area vector normal to the surface.

The SI unit of current density is A/m².

Its dimensional formula is:

[j] = [A L⁻²]

Current density is a vector. Its direction is the direction of conventional current.

Drift Velocity and Mobility Current Electricity Notes

Free electrons in a conductor are always in rapid random motion. A steady current appears only when an electric field creates a small average drift.

Motion of Electrons Without an Electric Field

Without an applied electric field, electrons move randomly because of thermal motion.

Their velocities have no preferred direction. Therefore, the average velocity of all free electrons is zero.

Average velocity = 0

Hence, random thermal motion alone does not produce an electric current.

Drift of Electrons in an Electric Field

When an electric field E is applied, each electron experiences a force:

F = −eE

Its acceleration is:

a = −eE/m

Here:

• e is the magnitude of electron charge.
• m is the mass of an electron.
• The negative sign shows motion opposite to E.

Electrons collide repeatedly with the positive ions of the conductor. Their average velocity due to the field is called drift velocity.

vd = −eEτ/m

For magnitude:

vd = eEτ/m

Here, τ is the average time between two successive collisions.

Relation Between Current and Drift Velocity

Consider a conductor with:

• Cross-sectional area A
• Free-electron number density n
• Drift-speed magnitude vd
• Electron charge magnitude e

In time Δt, electrons within length vdΔt cross the section.

Number of electrons crossing:

N = nAvdΔt

Total charge crossing:

Q = neAvdΔt

Therefore:

I = Q/Δt

I = neAvdA

Thus:

vd = I/(neA)

Current density is:

j = I/A

Therefore:

j = nevd

In vector form for electrons:

j = −nev­d

The conventional-current direction remains opposite to electron drift.

Relaxation Time and Mobility

Relaxation time τ is the average time between successive collisions of a conduction electron.

Mobility is the magnitude of drift velocity produced per unit electric field.

μ = vd/E

Using vd = eEτ/m:

μ = eτ/m

The SI unit of mobility is:

m² V⁻¹ s⁻¹

Ohm’s Law, Resistance and Resistivity Revision Notes

Ohm’s law connects potential difference with current. Its microscopic form connects electric field with current density.

Ohm’s Law

At a constant physical state, current through a conductor is directly proportional to the potential difference across it.

V ∝ I

Therefore:

V = IR

Here, R is the resistance of the conductor.

Ohm’s law requires R to remain independent of the applied voltage and current.

The V-I graph of an ohmic conductor is a straight line through the origin.

Resistance of a Conductor

Resistance is the opposition offered by a conductor to electric current.

R = V/I

The SI unit of resistance is ohm.

1 Ω = 1 V/A

Resistance depends on:

• Length of the conductor
• Cross-sectional area
• Material
• Temperature

For a uniform conductor:

R ∝ l

R ∝ 1/A

Combining both:

R = ρl/A

Here, ρ is the resistivity of the material.

Resistivity and Conductivity

Resistivity is a property of the material. It does not depend on the dimensions of a uniform conductor.

ρ = RA/l

Its SI unit is ohm metre.

The dimensional formula of resistivity is:

[ρ] = [M L³ T⁻³ A⁻²]

Conductivity is the reciprocal of resistivity.

σ = 1/ρ

Its SI unit is:

Ω⁻¹ m⁻¹

or

S m⁻¹

Microscopic Form of Ohm’s Law

Current density is:

j = nevd

Using:

vd = eEτ/m

We get:

j = ne²τE/m

Therefore:

j = σE

where:

σ = ne²τ/m

Since ρ = 1/σ:

E = ρj

These relations form the microscopic version of Ohm’s law.

Limitations of Ohm’s Law

Ohm’s law does not apply universally.

A device may be non-ohmic when:

• V is not directly proportional to I.
• Current depends on the direction of applied voltage.
• More than one voltage value corresponds to the same current.
• Resistance changes with voltage, temperature or current.

A diode has a non-linear and direction-dependent V-I characteristic.

The equation R = V/I can still define resistance at a point. This alone does not prove that a device follows Ohm’s law.

Resistivity of Materials and Temperature Dependence Notes

Materials differ greatly in resistivity. Temperature also affects the motion and number of charge carriers.

Conductors, Semiconductors and Insulators

Metals generally have resistivities from about 10⁻⁸ Ω m to 10⁻⁶ Ω m.

Insulators can have resistivities many orders of magnitude higher.

Temperature Dependence of Metallic Resistivity

Over a limited temperature range:

ρT = ρ₀[1 + α(T − T₀)]

Here:

• ρT is resistivity at temperature T.
• ρ₀ is resistivity at reference temperature T₀.
• α is the temperature coefficient of resistivity.

For metals, α is positive.

As temperature rises, lattice vibrations increase. Electrons suffer more frequent collisions, so relaxation time decreases and resistivity increases.

Temperature Dependence of Semiconductor Resistivity

For semiconductors, resistivity generally decreases with temperature.

A temperature rise produces more charge carriers. This increase is greater than the effect of more frequent collisions.

Alloys such as nichrome, manganin and constantan have a weak temperature dependence. They are useful where nearly constant resistance is required.

Combination of Resistors Current Electricity Revision Notes

Resistors are combined to obtain a required equivalent resistance. The circuit behaviour depends on whether the connection is series or parallel.

Resistors in Series

In a series combination:

• The same current flows through every resistor.
• Potential differences add.
• Equivalent resistance is greater than each individual resistance.

V = V₁ + V₂ + V₃

Using V = IR:

IRs = IR₁ + IR₂ + IR₃

Therefore:

Rs = R₁ + R₂ + R₃

For n resistors:

Rs = R₁ + R₂ + … + Rn

For n equal resistors of resistance R:

Rs = nR

Resistors in Parallel

In a parallel combination:

• The same potential difference appears across each resistor.
• Currents in individual branches add.
• Equivalent resistance is less than the smallest resistance.

I = I₁ + I₂ + I₃

Using I = V/R:

V/Rp = V/R₁ + V/R₂ + V/R₃

Therefore:

1/Rp = 1/R₁ + 1/R₂ + 1/R₃

For two resistors:

Rp = R₁R₂/(R₁ + R₂)

For n equal resistors:

Rp = R/n

Series and Parallel Resistance Comparison

Electrical Energy and Power Class 12 Chapter 3 Notes

A source supplies energy to maintain current. In a resistor, this electrical energy changes mainly into heat.

Electrical Energy

When charge Q moves through potential difference V:

W = VQ

Since Q = It:

W = VIt

Using V = IR:

W = I²Rt

Also:

W = V²t/R

The SI unit of electrical energy is joule.

Electrical Power

Electrical power is the rate at which electrical energy is supplied or dissipated.

P = W/t

Therefore:

P = VI

Using Ohm’s law:

P = I²R

P = V²/R

The SI unit of power is watt.

1 W = 1 J/s

Power Transmission and Ohmic Loss

Transmission cables have resistance Rc.

Power lost in the cables is:

Pc = I²Rc

For transmitted power P:

P = VI

Therefore:

I = P/V

Substituting:

Pc = P²Rc/V²

For a fixed transmitted power, power loss decreases as transmission voltage increases.

This is why electrical power is transmitted at a high voltage and low current.

Cells, EMF and Internal Resistance Current Electricity Notes

A cell maintains a potential difference by converting chemical energy into electrical energy.

Electromotive Force

The electromotive force of a cell is the work done by the cell per unit charge in moving charge through the complete circuit.

ε = W/q

Its SI unit is volt.

EMF equals the terminal potential difference when the circuit is open and no current flows.

Terminal Potential Difference

A real cell has internal resistance r.

When current I flows from the cell:

V = ε − Ir

Here:

• ε is the EMF.
• Ir is the potential drop inside the cell.
• V is the terminal voltage.

When the cell is being charged:

V = ε + Ir

Current Supplied by a Cell

Consider a cell of EMF ε and internal resistance r connected to external resistance R.

The total resistance is:

R + r

Therefore:

I = ε/(R + r)

The terminal potential difference is:

V = IR

It is also:

V = ε − Ir

For R = 0:

Imax = ε/r

This is the theoretical short-circuit current.

Cells in Series

For cells connected in the same direction:

εeq = ε₁ + ε₂ + … + εn

req = r₁ + r₂ + … + rn

For n identical cells:

εeq = nε

req = nr

Current through external resistance R:

I = nε/(R + nr)

If cells oppose each other, their EMFs are added algebraically with signs.

Cells in Parallel

For two unequal cells connected in parallel:

1/req = 1/r₁ + 1/r₂

Therefore:

req = r₁r₂/(r₁ + r₂)

The equivalent EMF is:

εeq = (ε₁/r₁ + ε₂/r₂)/(1/r₁ + 1/r₂)

For n cells:

1/req = 1/r₁ + 1/r₂ + … + 1/rn

εeq/req = ε₁/r₁ + ε₂/r₂ + … + εn/rn

For n identical cells:

εeq = ε

req = r/n

Current through external resistance R:

I = ε/(R + r/n)

Series and Parallel Cells Comparison

Kirchhoff’s Rules for Electrical Circuits Revision Notes

Simple series and parallel formulas cannot solve every electrical network. Kirchhoff’s rules handle circuits with several branches and cells.

Junction Rule

At any junction, the sum of currents entering equals the sum leaving.

ΣIin = ΣIout

For example:

I₁ + I₂ = I₃ + I₄

This rule follows from conservation of electric charge.

No net charge accumulates at a junction in a steady-current circuit.

Loop Rule

The algebraic sum of potential changes around any closed loop is zero.

ΣΔV = 0

For a loop containing resistors and cells:

Σε − ΣIR = 0

The loop rule follows from conservation of energy.

After moving around a closed loop, the final potential must equal the starting potential.

Sign Conventions for Circuit Equations

Across a resistor:

• Moving in the direction of current: potential change = −IR
• Moving opposite to current: potential change = +IR

Across a cell:

• Moving from negative to positive terminal: potential change = +ε
• Moving from positive to negative terminal: potential change = −ε

A negative current obtained after solving means the actual direction is opposite to the assumed arrow.

Wheatstone Bridge Class 12 Physics Notes

A Wheatstone bridge uses four resistors and a galvanometer. It helps determine an unknown resistance through a null-deflection condition.

Wheatstone Bridge Arrangement

The bridge contains four resistors R₁, R₂, R₃ and R₄.

• A cell is connected across one diagonal.
• A galvanometer is connected across the other diagonal.
• Current through the galvanometer is represented by Ig.

The bridge is balanced when:

Ig = 0

At balance, the two galvanometer junctions have the same potential.

Balanced Wheatstone Bridge Condition

For a balanced Wheatstone bridge:

R₁/R₂ = R₃/R₄

It can also be written as:

R₁R₄ = R₂R₃

If three resistances are known, the fourth can be calculated.

For example:

R₄ = R₂R₃/R₁

The balance condition does not depend on the resistance of the galvanometer because no current flows through it at balance.

Current Electricity Formula Notes

Important Terms in Class 12 Physics Chapter 3

Revise Current Electricity Notes in 30 Minutes

Divide a 30-minute revision into three parts:

• First 10 minutes: Current, current density, drift velocity and Ohm’s law
• Next 10 minutes: Resistivity, resistor combinations, power and cells
• Final 10 minutes: Kirchhoff’s rules, Wheatstone bridge and formulas

While solving numericals, check the assumed current direction and sign of each potential change.

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