Resistivity and internal resistance

Resistance depends on the material and shape of a conductor: longer, thinner wires resist more. Real batteries also have internal resistance, so their voltage drops when they supply current.

Key facts

  • R = ρL/A (ρ is resistivity in Ωm).
  • e.m.f. ε: energy given to each coulomb by the source.
  • ε = I(R + r), where r is internal resistance.
  • Terminal p.d. V = ε − Ir.

Worked examples

Example 1

A battery of e.m.f. 9 V and internal resistance 0.5 Ω is connected to a 4 Ω resistor. Find the current and terminal p.d.

  1. I = 9 ÷ 4.5 = 2 A
  2. V = 9 − 2 × 0.5 = 8 V

Answer: 2 A and 8 V