Current Electricity: Drift, Resistance, Kirchhoff and the Potentiometer
Current Electricity tests how charge flow is modelled microscopically (drift velocity, mobility, relaxation time) and how circuits are solved using Kirchhoff's rules, the Wheatstone bridge, the metre bridge and the potentiometer.
Core rules
- I = nAev(d); current density J = I/A = nev(d) = σE; resistivity ρ = m/(ne²τ) and conductivity σ = 1/ρ.
- Resistance R = ρl/A. For metals ρ rises with temperature; for semiconductors and electrolytes it falls.
- Kirchhoff's rules: junction rule ΣI = 0 (charge conservation); loop rule ΣΔV = 0 (energy conservation).
- Terminal voltage V = ε − Ir while discharging, and V = ε + Ir while being charged.
- Wheatstone bridge balances when P/Q = R/S; the metre bridge is its practical laboratory form.
- A potentiometer compares emfs at zero current: ε₁/ε₂ = l₁/l₂, which is why it measures emf, not terminal voltage.
Worked example
A cell of emf 2.0 V and internal resistance 0.5 Ω is joined to a 4.5 Ω resistor. The current is I = ε/(R+r) = 2.0/5.0 = 0.40 A. The terminal voltage is V = ε − Ir = 2.0 − 0.40 × 0.5 = 1.80 V, the drop across the external resistor, and the power wasted inside the cell is I²r = 0.08 W.
Traps
Adding internal resistance to the external branch alone; sign errors when a loop crosses a cell from − to +; treating the potentiometer as drawing current at balance; mixing the rules for cells in series (emfs add) with parallel combinations of unequal emfs.