Internal resistance: (b) terminal p.d.; 'lost volts'

The idea

Terminal p.d. is the potential difference across the external circuit, measured between the terminals of a source when current flows. 'Lost volts' is the potential difference across the internal resistance of the source, equal to Ir, where I is the current and r is the internal resistance. The relationship is terminal p.d. = e.m.f. - lost volts, or V = ε - Ir.

For example: A cell with ε = 1.5 V and r = 0.50 Ω delivering a current of 2.0 A has lost volts = 2.0 × 0.50 = 1.0 V, so terminal p.d. = 1.5 - 1.0 = 0.50 V. When no current flows, lost volts is zero and terminal p.d. equals e.m.f.

What earns the marks

• Define terminal p.d. as the potential difference across the external circuit when current flows.
• Define 'lost volts' as the potential difference across the internal resistance, equal to Ir.
• State the relationship terminal p.d. = e.m.f. - lost volts, or V = ε - Ir.
• Calculate terminal p.d. or lost volts given e.m.f., current and internal resistance.
• Explain that terminal p.d. equals e.m.f. when no current flows (open circuit).

Common mistakes and how to put them right

• Thinking that terminal p.d. is always equal to e.m.f.

  Put it right: Terminal p.d. is less than e.m.f. when current flows due to lost volts.

• Confusing 'lost volts' with energy lost.

  Put it right: 'lost volts' is a potential difference, not energy, though it represents energy dissipated per unit charge inside the source.

• Forgetting to include internal resistance when calculating terminal p.d.

  Put it right: Subtract Ir from e.m.f. to find terminal p.d. when current flows.

• Assuming lost volts is constant.

  Put it right: Lost volts depends on current, so it varies with the external circuit.

Exam tips

• Use V = ε - Ir to find terminal p.d. quickly.
• Remember that lost volts = Ir, so if current is zero, lost volts is zero.
• Check units: e.m.f., terminal p.d. and lost volts are all in volts.