Class 12 · Chapter 3

Current Electricity

Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.

Current Electricity Short Notes

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Condensed revision points for Current Electricity — for quick recall before exams, not a substitute for the full notes.

I = dQ/dt; scalar, SI unit ampere (1 A = 1 C/s).
Conventional current direction = direction of positive charge flow, opposite to electron drift.
J = dI/dA (area normal to flow); general form dI = J dA cosθ.
J is a vector, direction same as E⃗; unit A/m².
Steady current in a non-uniform wire: I is constant everywhere, but J, E, v_d ∝ 1/A.

v_rms = √(3kT/m); order 10⁵ m/s at room temperature — but average velocity of free electrons is zero without a field.
Drift velocity v_d = eEτ/m; order 10⁻⁴ m/s (~10⁹ times slower than thermal speed).
I = neAv_d — current in terms of free-electron density, area, and drift speed.
n (free e⁻ density) ≈ 10²⁸ /m³ in metals; ≈ 10¹⁶ /m³ in semiconductors.
Mobility μ = v_d/E = eτ/m; unit m²/(V·s); always taken positive.
Mean free path λ ≈ 10 Å; relaxation time τ ≈ 10⁻¹⁴ s in metals.

Microscopic: J⃗ = σE⃗, σ = ne²τ/m. Macroscopic: V = IR.
R = ρl/A; ρ = 1/σ. ρ depends only on material & temperature — never on shape/size.
Ohm's law is empirical, not fundamental — fails for diodes, vacuum tubes, GaAs.
Stretch to n× length (volume const): R → n²R. Radius → (1/n): R → n⁴R.
Small length change x% (volume const) ⟹ resistance changes by ≈ 2x%.

ρ_T = ρ₀[1 + α(T−T₀)]; R_t = R₀(1 + αΔT).
α > 0 for metals (resistance rises with T). α < 0 for semiconductors, insulators, carbon.
Below critical temperature, some conductors lose all resistance — superconductors.
Resistor colour bands: digit, digit, multiplier, tolerance. Gold = ±5%, Silver = ±10%, no band = ±20%.
Manganin/constantan used in resistance boxes — near-zero α, stable resistance with temperature.

Series: R = R₁+R₂+R₃; same current; V₁:V₂:V₃ = R₁:R₂:R₃.
Parallel: 1/R = 1/R₁+1/R₂+1/R₃; same voltage; I₁:I₂:I₃ = 1/R₁:1/R₂:1/R₃.
Equivalent resistance in parallel < smallest individual resistance.
Mixed networks: successive reduction, symmetry (equipotential points), or nodal method for short-circuited points.

Junction law (KCL): ΣI = 0 — based on conservation of charge.
Loop law (KVL): ΣIR = ΣE around a closed loop — based on conservation of energy.
Sign rule: emf positive when moving − to + inside a cell; IR drop negative when moving along assumed current direction.

I = E/(R+r). Discharging: V = E − Ir. Charging: V = E + Ir.
Open circuit (R→∞): I = 0, V = E (max terminal voltage).
Short circuit (R=0): I = E/r (max current), V = 0.
r depends on electrode separation, electrolyte concentration, electrode area, temperature — not on external circuit.

n in series: E_net = nE, r_net = nr, I = nE/(nr+R). Best when nr ≪ R.
m identical in parallel: r_net = r/m, I = mE/(r+mR). Best when r ≫ mR.
n series × m parallel rows: E_net = nE, r_net = nr/m. Current max when R = nr/m.

Ammeter: low shunt resistance in parallel, R_shunt = I_gR_g/(I−I_g). Ideal ammeter R = 0.
Voltmeter: high resistance in series, R_series = V/I_g − R_g. Ideal voltmeter R = ∞.
Shunt reduces sensitivity but protects the coil and extends range.
Range I → nI: parallel resistor R_g/(n−1). Range V → nV: series resistor (n−1)R_g.

Balance condition: P/Q = R/S; galvanometer carries zero current at balance.
Metre bridge: S = R(100−l)/l, where l is the balance length from end A.
Potentiometer: zero current drawn at balance — more accurate than a voltmeter for emf/PD measurement.
Potential gradient x = V_AB/L. Comparing emfs: E₁/E₂ = l₁/l₂. Internal resistance: r = R(l₁−l₂)/l₂.
Sensitivity ↑ as x ↓ — achieved by increasing wire length or reducing primary current via rheostat.
Changes in the secondary (galvanometer) circuit never affect the potential gradient.

Drift velocity (~10⁻⁴ m/s) and thermal speed (~10⁵ m/s) are not the same thing — don't substitute one for the other.
Resistivity ρ is a material property; resistance R also depends on length and area — a 'longer wire has more resistivity' is wrong, it has more resistance.
In series, the dimmer-rated bulb (lower wattage) is the one that glows brighter — easy to get backwards under exam pressure.
EMF is the open-circuit terminal voltage, not the voltage you'll read with current flowing — V = E only when I = 0.
A potentiometer at balance draws zero current from the cell being measured; a voltmeter, however ideal, can never claim that.
Wheatstone bridge balance (P/Q = R/S) does not depend on the cell's emf or internal resistance — only on the four resistances.
Adding a shunt in parallel lowers the net resistance below the shunt value itself, not just below the galvanometer's resistance.

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