Current Electricity

Current, drift, and Ohm's law

Current I = dQ/dt, SI unit ampere (1 A = 1 C/s). At microscopic scale I = nAv_de, where n is electron density, A cross-section, v_d drift velocity, and e = 1.6×10⁻¹⁹ C. Ohm's law V = IR for ohmic materials. Resistance R = ρL/A, with ρ the resistivity. Copper has ρ ≈ 1.7×10⁻⁸ Ω·m at room temperature; a 1 m length of 1 mm² copper wire has R ≈ 0.017 Ω.

Resistor combinations

Series: R_eq = R₁ + R₂ + … (same current, voltages add). Parallel: 1/R_eq = 1/R₁ + 1/R₂ + … (same voltage, currents add). Two equal resistors in parallel halve the resistance; in series they double it. The classic MDCAT MCQ: three 6 Ω resistors — series gives 18 Ω, parallel gives 2 Ω.

Kirchhoff's laws

KCL (junction rule): sum of currents into a node = sum out (charge conservation). KVL (loop rule): sum of EMFs around a closed loop = sum of IR drops (energy conservation). For a single loop containing an EMF ε, an internal resistance r, and external R, the current is I = ε/(R+r). Terminal voltage V = ε − Ir; under open-circuit conditions V = ε.

Power and electrical energy

P = VI = I²R = V²/R. A 60 W bulb on 220 V draws I = 60/220 ≈ 0.27 A and has R = V²/P ≈ 807 Ω. Electrical energy is W = Pt; a 2 kW heater for 5 hours uses 10 kWh = 36 MJ. The kilowatt-hour MCQ recurs every other year — convert it as 1 kWh = 3.6×10⁶ J.

EMF, internal resistance, and meters

A real battery is modelled as ideal EMF ε in series with internal resistance r. Maximum power transfer to an external load occurs when R = r. An ammeter is a low-resistance device placed in series; a voltmeter is high-resistance, placed in parallel. Galvanometers are converted by adding shunts (ammeter) or multipliers (voltmeter). Wheatstone bridge balance condition: P/Q = R/S, used to measure unknown resistance precisely. References: HRW Chapters 26-27, Serway 27-28, FSc Chapter 13-14.