Current Electricity: Resistance, Circuits and Cells
What this domain tests
Current electricity tests Ohm's law, resistivity and drift speed, Kirchhoff's rules, the Wheatstone bridge and potentiometer, and cells with internal resistance.
Core rules
- R = ρL/A; resistivity rises with temperature for metals and falls for semiconductors.
- Drift velocity v_d = I/(nAe); the current is the same everywhere in a series wire even though drift speed changes with area.
- Kirchhoff: junction ΣI = 0; loop ΣIR = Σε, taking care with sign direction.
- Cell on discharge: terminal V = ε − Ir, and I = ε/(R + r). Maximum power is delivered to the load when R = r.
- Wheatstone bridge balances when P/Q = R/S; a potentiometer compares emfs at null deflection, drawing no current from the cell being tested.
Worked example
A copper wire of cross-section 1.0 mm² carries 1.0 A. Taking n = 8.5×10²⁸ m⁻³, find the drift speed. v_d = I/(nAe) = 1.0/[(8.5×10²⁸)(1.0×10⁻⁶)(1.6×10⁻¹⁹)] = 1.0/(1.36×10⁴) ≈ 7.4×10⁻⁵ m/s. Note that 1 mm² = 1×10⁻⁶ m². The drift speed is under 0.1 mm/s, yet the bulb lights instantly because the electric field is established at nearly the speed of light.
Traps that cost marks
- Confusing drift speed with the speed of the electrical signal.
- Using the diameter as the radius in A = πr².
- Writing V = ε + Ir for a discharging cell.
- Forgetting that a balanced bridge or potentiometer needs zero galvanometer current, not maximum current.