Current Electricity Class 12 Notes (2026-27) — CBSE
Class 12 Physics Chapter 3 notes: drift velocity, Ohm's law, resistivity, EMF and internal resistance, Kirchhoff's laws and the Wheatstone bridge.
Current Electricity — Class 12 Physics Notes
Chapter Snapshot
This chapter explains how charge flows in conductors and circuits: drift velocity and its link to current, Ohm's law and resistivity, the role of a cell's EMF and internal resistance, and the two circuit-analysis tools — Kirchhoff's laws and the Wheatstone bridge.
Board relevance: ~7 marks. Expect a Kirchhoff/circuit numerical and an EMF-internal-resistance question. The formulas are compact; most marks come from applying the sign conventions correctly.
Syllabus note (rationalised): the Meter Bridge and Potentiometer sections have been removed. Focus on Kirchhoff's laws and the Wheatstone bridge.
Key Concepts & Definitions
Electric current I = Q/t (unit ampere). At the microscopic level, current is due to the drift of free electrons.
Drift velocity (vd) — the small average velocity electrons acquire opposite to the applied field:
vd = eEτ/m and I = neAvd
where n = number density of free electrons, e = electron charge, A = area, τ = relaxation time.
Mobility μ = vd/E (drift velocity per unit field).
Current density J = I/A = σE (a vector along the field).
Formulas — Ohm's Law and Resistance
Ohm's law: V = IR (at constant temperature).
Quantity Formula
Resistance from dimensions R = ρL/A
Conductivity σ = 1/ρ
Resistivity in terms of n, τ ρ = m/(ne²τ)
Temperature dependence ρT = ρ₀[1 + α(T − T₀)]
- For conductors, ρ increases with temperature (α positive); for semiconductors, ρ decreases (α negative).
- Series: R = R₁ + R₂ + … (same current). Parallel: 1/R = 1/R₁ + 1/R₂ + … (same voltage).
EMF, Internal Resistance and Cells
EMF (ε) — potential difference across a cell on open circuit (no current).
Terminal voltage (V) — potential difference when current I flows:
V = ε − Ir (discharging) ; V = ε + Ir (while being charged)
where r is the internal resistance. Current in a single-cell circuit: I = ε/(R + r).
Cells in series (n cells): εeq = nε, req = nr → I = nε/(R + nr).
Cells in parallel (n identical cells): εeq = ε, req = r/n → I = ε/(R + r/n).
Kirchhoff's Laws and the Wheatstone Bridge
Kirchhoff's junction (current) rule: the sum of currents entering a junction = sum leaving (ΣI = 0). Based on conservation of charge.
Kirchhoff's loop (voltage) rule: the algebraic sum of potential differences around any closed loop is zero (ΣV = 0). Based on conservation of energy.
Wheatstone bridge: four resistors P, Q, R, S in a diamond with a galvanometer across the middle. It is balanced (galvanometer reads zero) when:
P/Q = R/S
At balance, an unknown resistance can be found from the other three. No current flows through the galvanometer branch.
Worked Examples
Example 1 — Drift velocity link: A copper wire (n = 8.5 × 10²⁸ /m³, A = 2 × 10⁻⁶ m²) carries 3 A. Find vd.
vd = I/(neA) = 3 / [(8.5 × 10²⁸)(1.6 × 10⁻¹⁹)(2 × 10⁻⁶)] ≈ 1.1 × 10⁻⁴ m/s (very slow — electrons drift, the field sets up almost instantly).
Example 2 — Internal resistance: A cell of EMF 2 V and internal resistance 0.5 Ω drives a 3.5 Ω resistor. Find the current and terminal voltage.
I = ε/(R + r) = 2/(3.5 + 0.5) = 0.5 A. V = ε − Ir = 2 − 0.5(0.5) = 1.75 V.
Example 3 — Wheatstone bridge: In a balanced bridge, P = 10 Ω, Q = 20 Ω, R = 15 Ω. Find S.
P/Q = R/S → 10/20 = 15/S → S = 15 × 20/10 = 30 Ω.
Example 4 — Cells in series: Three cells each ε = 1.5 V, r = 0.5 Ω in series drive a 3 Ω resistor.
I = nε/(R + nr) = 4.5/(3 + 1.5) = 1 A.
Important Question Patterns
1. Drift velocity/current (2–3 marks): I = neAvd; explain why drift velocity is small yet current flows quickly.
2. Resistivity (2 marks): R = ρL/A; effect of stretching a wire; temperature dependence for conductors vs semiconductors.
3. EMF & internal resistance (3 marks): find I, terminal voltage, or r; V–I graph of a cell (intercept ε, slope −r).
4. Kirchhoff's laws (3–5 marks): set up junction and loop equations for a two-loop network and solve for the branch currents.
5. Wheatstone bridge (2–3 marks): balance condition P/Q = R/S; find an unknown resistance.
⚡ Quick Revision
- I = neAvd; drift velocity vd = eEτ/m; mobility μ = vd/E; current density J = σE.
- Ohm's law V = IR; R = ρL/A; σ = 1/ρ; ρ = m/(ne²τ). Conductor ρ ↑ with T, semiconductor ρ ↓.
- Terminal voltage V = ε − Ir (discharge); I = ε/(R + r). Series cells: nε, nr. Parallel: ε, r/n.
- Kirchhoff: junction ΣI = 0 (charge), loop ΣV = 0 (energy).
- Wheatstone balance: P/Q = R/S (galvanometer reads zero).
- Removed from syllabus: meter bridge and potentiometer.
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