Current Electricity Class 12 Physics Notes 2026-27 | CBSE Chapter 3

Current Electricity — Class 12 Physics, Chapter 3

These notes are designed for CBSE Class 12 Physics 2026–27 and follow the official Chapter 3 scope. The aim is not just to memorise formulas, but to understand the circuit logic needed for board-style conceptual questions and numericals.

CBSE 2026–27 scope covered here: electric current and flow of charge in metallic conductors; drift velocity and mobility and their relation with current; Ohm's law and V–I characteristics; electrical energy and power; resistivity and conductivity; temperature dependence of resistance; emf, potential difference and internal resistance; cells in series and parallel; Kirchhoff's rules; and Wheatstone bridge.

The official CBSE curriculum places Chapter 3 under Unit II: Current Electricity, which carries 17 marks at unit level. CBSE does not publish a fixed Chapter-3-only mark allocation in the curriculum.

Quick Navigation

1. Electric Current and Flow of Charge
2. Drift Velocity, Mobility and Current
3. Ohm's Law and V–I Characteristics
4. Resistance, Resistivity and Conductivity
5. Temperature Dependence of Resistance
6. Electrical Energy and Power
7. EMF, Potential Difference and Internal Resistance
8. Cells in Series and Parallel
9. Kirchhoff's Rules
10. Wheatstone Bridge
11. Formula Map
12. Common Exam Traps
13. How to Study This Chapter

1. Electric Current and Flow of Charge

Electric current is the rate of flow of electric charge through a cross-section of a conductor.

I = Q/t    (for steady current)

More generally, when the current changes with time:

I = dQ/dt

• SI unit of current: ampere (A).
• 1 A means 1 coulomb of charge crossing a cross-section per second.
• Conventional current is taken in the direction of motion of positive charge.
• In a metallic conductor, the mobile charge carriers are electrons, whose drift is opposite to the conventional current.

Current density

Current density is the current flowing per unit area of cross-section normal to the flow.

J = I/A

For a uniform current distribution, the current density has the same magnitude over the relevant cross-section.

Concept check: A wire can carry a large current even though the drift speed of electrons is very small. The current depends on the number density of charge carriers, their charge, cross-sectional area and drift velocity.

2. Drift Velocity, Mobility and Current

In a metal, free electrons undergo random thermal motion. In the absence of an applied electric field, their random motion produces no net current. When an electric field is established, the electrons acquire a small average velocity called drift velocity.

Drift velocity

Drift velocity is the average velocity acquired by charge carriers due to an applied electric field. For electrons, its direction is opposite to the electric field.

In the simple microscopic model:

v_d = eEτ/m

where e is the magnitude of electronic charge, E is electric field, τ is mean relaxation time and m is electron mass.

Mobility

Mobility measures the drift speed acquired per unit electric field.

μ = v_d/E = eτ/m

Thus, for a given material and temperature in the simple model, mobility connects the applied electric field with the magnitude of drift velocity.

Relation between current and drift velocity

If n is the number of free charge carriers per unit volume, A is cross-sectional area and e is the magnitude of charge on each carrier:

I = neAv_d

Therefore:

J = nev_d

Combining this with mobility gives the microscopic form of conductivity:

J = neμE    and    σ = neμ

Exam trap: Do not say that electrons move from positive to negative terminal in the same sense as conventional current. In a metal, electron drift is opposite to conventional current.

3. Ohm's Law and V–I Characteristics

Ohm's law: At constant physical conditions such as temperature, the current through a conductor is directly proportional to the potential difference across it.

V ∝ I    ⇒    V = IR

Here R is the resistance of the conductor under those conditions.

What the V–I graph tells you

• For an ohmic conductor at constant temperature, the V–I graph is a straight line through the origin.
• On a V-versus-I graph, the slope is resistance: R = ΔV/ΔI.
• On an I-versus-V graph, the slope is conductance: G = ΔI/ΔV = 1/R.

Ohmic and non-ohmic behaviour

Ohm's law is not a universal law for every electrical device. A device is non-ohmic when its V–I relation is not linear under the conditions being considered.

Remember: “Resistance” can still be defined at a particular operating point for a nonlinear device, but the simple constant-resistance relation V = IR does not describe the entire V–I curve.

4. Resistance, Resistivity and Conductivity

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

R = ρL/A

where ρ is resistivity, L is length and A is cross-sectional area.

Resistivity

Resistivity is a material property. For a given material at a specified temperature, it does not depend on the dimensions of the particular sample.

ρ = RA/L

• SI unit: Ω m.
• Resistance depends on both material and geometry.
• Resistivity mainly characterises the material and its physical condition, including temperature.

Conductivity

Conductivity is the reciprocal of resistivity.

σ = 1/ρ

SI unit of conductivity: S m⁻¹.

Changing the dimensions of a wire

If the same material is stretched without changing its volume, its length and area change in opposite ways. This is a common numerical pattern.

Useful reasoning: Never assume resistance stays unchanged merely because the material stays the same. Geometry matters through R = ρL/A.

5. Temperature Dependence of Resistance

For many metallic conductors over a limited temperature range, resistance changes approximately linearly with temperature:

R_T = R₀[1 + α(T − T₀)]

Here R₀ is resistance at reference temperature T₀ and α is the temperature coefficient of resistance for that range.

• For typical metals, resistance increases as temperature rises.
• The linear relation is an approximation over a suitable temperature range.
• Do not apply the same temperature trend blindly to every material.

Graph idea

For a metal in the approximately linear range, a graph of resistance against temperature has a positive slope.

Common mistake: Resistivity and resistance are related, but they are not the same physical quantity. A temperature change can alter resistivity, which then changes the resistance of a given sample.

6. Electrical Energy and Power

Electrical power is the rate at which electrical energy is transferred or converted.

P = VI

Using Ohm's law for a resistor:

P = I²R = V²/R

Electrical energy supplied or consumed in time t is:

W = Pt = VIt = I²Rt = V²t/R

Units

• Power: watt (W).
• Energy: joule (J).
• Commercial electrical energy is commonly measured in kilowatt-hour (kWh).
• 1 kWh = 3.6 × 10⁶ J.

Numerical shortcut: Before selecting a power formula, identify what the question gives—V, I and R. Then use the form that minimises unnecessary calculation.

7. EMF, Potential Difference and Internal Resistance

EMF

The emf of a cell is the energy supplied by the source per unit charge when the source drives charge through the complete circuit. It is represented by ε.

Internal resistance

A real cell has internal resistance, represented by r. When current flows through a cell delivering current to an external circuit, some potential is lost inside the cell.

V = ε − Ir

where V is the terminal potential difference while the cell is supplying current I.

For an external resistance R connected to a cell:

I = ε/(R + r)

and the terminal voltage is:

V = IR = εR/(R + r)

Cell being charged

When current is forced into a cell in the charging direction, the terminal potential difference can exceed the emf:

V = ε + Ir

Exam trap: Do not automatically write V = ε − Ir in every situation. The sign depends on whether the cell is delivering current or being charged.

8. Cells in Series and Parallel

Identical cells in series

For n identical cells, each of emf ε and internal resistance r, connected in series aiding:

ε_eq = nε     r_eq = nr

With external resistance R:

I = nε/(R + nr)

Identical cells in parallel

For n identical cells connected in parallel:

ε_eq = ε     r_eq = r/n

Hence:

I = ε/(R + r/n)

Choosing series or parallel

• Series increases the effective emf but also increases internal resistance.
• Parallel keeps the emf equal to that of one cell while reducing equivalent internal resistance for identical cells.
• The useful arrangement depends on the external resistance and the required current.

Problem-solving habit: First replace the cell combination by its equivalent emf and equivalent internal resistance. Then treat the rest of the circuit normally.

9. Kirchhoff's Rules

Kirchhoff's rules are used when a circuit cannot be handled conveniently by simple series-parallel reduction.

Kirchhoff's Junction Rule

At any junction, the total current entering equals the total current leaving.

ΣI = 0

This expresses conservation of charge.

Kirchhoff's Loop Rule

For any closed loop, the algebraic sum of potential changes is zero.

ΣΔV = 0

This expresses conservation of energy.

Sign convention for loop equations

• Across a resistor in the direction of assumed current: potential change = −IR.
• Across a resistor opposite to assumed current: potential change = +IR.
• Across a cell from negative to positive terminal: +ε.
• Across a cell from positive to negative terminal: −ε.

Reliable method for Kirchhoff numericals

1. Draw the circuit clearly.
2. Assign a current direction to each branch. The initial choice may be arbitrary.
3. Mark the polarity of each cell.
4. Apply the junction rule where required.
5. Choose independent loops and apply the loop rule.
6. Solve the simultaneous equations.
7. If a current comes out negative, its actual direction is opposite to the assumed direction.

Important: A negative current is not an incorrect answer by itself. It usually means the chosen reference direction was opposite to the actual current direction.

10. Wheatstone Bridge

A Wheatstone bridge is a network of four resistances used to determine an unknown resistance under a balance condition.

For the standard arrangement with resistances P, Q, R and S, the bridge is balanced when no current flows through the galvanometer.

P/Q = R/S

Equivalently:

PS = QR

What “balanced” means

• The potentials at the two galvanometer junctions are equal.
• Therefore the potential difference across the galvanometer is zero.
• Hence the galvanometer current is zero.

How to solve bridge problems

1. Identify the four arms of the bridge.
2. Match them carefully to the ratio in the circuit diagram.
3. Apply the balance condition only when the galvanometer current is zero.
4. Substitute the known resistances and solve for the unknown.

Do not confuse: Wheatstone bridge balance is a ratio condition. It is not the same as simply saying that two resistors are equal.

11. Current Electricity Formula Map

Concept	Key relation
Current	I = Q/t; I = dQ/dt
Current density	J = I/A
Drift velocity	vd = eEτ/m
Mobility	μ = vd/E = eτ/m
Current and drift	I = neAvd
Conductivity	σ = 1/ρ = neμ
Ohm's law	V = IR
Resistance	R = ρL/A
Temperature dependence	RT = R0[1 + α(T − T0)]
Power	P = VI = I²R = V²/R
Electrical energy	W = Pt = VIt = I²Rt = V²t/R
Cell supplying current	V = ε − Ir
Cell current	I = ε/(R+r)
Identical cells in series	εeq = nε; req = nr
Identical cells in parallel	εeq = ε; req = r/n
Junction rule	ΣI = 0
Loop rule	ΣΔV = 0
Wheatstone balance	P/Q = R/S

12. Common Exam Traps

• ✓Confusing conventional current with electron drift direction.
• ✓Using V = IR for a nonlinear device without checking its conditions.
• ✓Confusing resistance with resistivity.
• ✓Forgetting that resistance depends on length and area.
• ✓Using the wrong sign for emf or IR in Kirchhoff loop equations.
• ✓Assuming a negative Kirchhoff current means the whole calculation is wrong.
• ✓Using V = ε − Ir when the cell is actually being charged.
• ✓Applying the Wheatstone balance ratio to a non-balanced bridge.
• ✓Using a chapter-specific mark claim when CBSE has only provided unit-level marks.
• ✓Mixing syllabus topics from older editions or competitive-exam material into a CBSE-only revision plan.

13. How to Study Current Electricity

Use this sequence rather than memorising the formula list first:

1. Build the microscopic picture: current → drift velocity → mobility → current density.
2. Move to circuit behaviour: Ohm's law → resistance → resistivity → temperature dependence.
3. Master power: connect V, I and R through the three equivalent power forms.
4. Understand real sources: emf → internal resistance → terminal voltage.
5. Practise cell combinations: derive equivalent emf and internal resistance before calculating current.
6. Learn circuit equations: junction rule → loop rule → simultaneous equations.
7. Finish with Wheatstone bridge: understand the balance condition before solving numerical questions.

Board-preparation checklist: You should be able to explain every formula in words, identify the physical quantity represented by each symbol, draw or interpret a V–I graph, solve a basic cell/internal-resistance problem, write correct Kirchhoff equations, and apply the Wheatstone balance condition without relying on memorised answer patterns.

14. Continue Your Physics Preparation

Chapter 1: Electric Charges and Fields Chapter 2: Electrostatic Potential and Capacitance

This page intentionally links only to resources that are already published and verified.

15. Official CBSE Resources

• CBSE Physics Curriculum 2026–27
• CBSE Class XII Sample Question Papers & Marking Schemes 2026–27
• CBSE Question Paper Archive

Source note: The syllabus scope and unit-level marks on this page are based on the official CBSE 2026–27 Physics curriculum. The chapter structure and study guidance have been written specifically for Learn Revise Hub. PYQs should be labelled as official only when their provenance is verified.