Current Electricity

Concept overview

Current I is the rate of flow of charge: I = dq/dt. Ohm's law V = IR holds for ohmic conductors — resistance R = ρL/A where ρ is resistivity. Series resistors add (R_s = ΣRᵢ); parallel resistors add reciprocally (1/R_p = Σ 1/Rᵢ). This is the mirror image of capacitor combinations.

Kirchhoff's rules generalise Ohm's law to arbitrary networks. The current rule (KCL) says currents at a junction sum to zero — a statement of charge conservation. The voltage rule (KVL) says the sum of voltage drops around any closed loop is zero — a statement of energy conservation. Together they let you solve any linear circuit.

The Wheatstone bridge is a classic four-resistor bridge with a galvanometer arm. When balanced, no current flows through the galvanometer, and the bridge condition R₁/R₂ = R₃/R₄ holds. This is used for precise resistance measurement. The potentiometer is a related device that measures unknown EMFs by comparing them against a known EMF along a uniform wire.

RC circuits introduce time dependence. When a capacitor is charged through a resistor from a source of EMF ε, the charge grows as Q(t) = Q_max(1 − e^(−t/RC)) with time constant τ = RC. On discharge, Q(t) = Q_0 e^(−t/RC).

Key formulas & concepts

• Ohm's law: V = IR
• Resistivity relation: R = ρL/A
• Series resistors: R_s = ΣRᵢ
• Parallel resistors: 1/R_p = Σ 1/Rᵢ
• KCL (junction rule): Σ I_in = Σ I_out
• KVL (loop rule): Σ ΔV around a closed loop = 0
• Wheatstone balance: R₁/R₂ = R₃/R₄
• RC time constant: τ = RC; Q(t) = Q₀(1 − e^(−t/RC))

Common mistakes to avoid

• Using Ohm's law for non-ohmic elements — diodes, transistors and semiconductor junctions don't obey V = IR.
• Forgetting internal resistance r of a battery — terminal voltage V = ε − Ir when current flows.
• Applying series-parallel rules to circuits with a bridge — Wheatstone-type circuits are not simple series-parallel.
• Confusing time constant τ = RC (charging) with the half-life of decay (τ ln 2).

JEE Main relevance

JEE Main asks 2 current-electricity problems every paper — usually one Wheatstone or Kirchhoff analysis and one RC-circuit or resistivity numerical.

JEE Advanced relevance

Advanced problems use Kirchhoff's rules on multi-loop networks with mesh analysis, or combine RC dynamics with capacitor-charge redistribution. Bridge circuits with a battery in the galvanometer arm are also standard.

Previous-year questions (PYQ)

Kirchhoff's rules and Wheatstone bridge are the two most-tested archetypes. Drill each in a focused PYQ session.