Explain why the terminal potential difference of a battery decreases as the external resistance in a circuit is decreased.

IB DP Physics Higher Level (2023 syllabus) — B.5 Current and circuits · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

A battery of electromotive force (emf) ε and internal resistance r is connected to an external resistor. The external resistance is gradually reduced.

Model answer (4 marks)

The current in the circuit is I=ε/(R+r). When R is reduced, I increases.
The internal resistance r causes a voltage drop of Ir.
As I rises, the drop Ir becomes larger.
The terminal potential difference is ε−Ir, so a larger Ir gives a smaller terminal pd.

Examiner tips

Show the formula I=ε/(R+r) and explain the effect of decreasing R. State that the internal drop is Ir and that it increases with I. Use the relation V_terminal=ε−Ir to link the two. Keep the answer concise and use the exact wording from the mark scheme.

Common mistakes

Confusing terminal pd with emf; forgetting the minus sign. Failing to mention that the drop is across the internal resistance. Using the wrong formula for current or ignoring the internal resistance.

Mark scheme (4 marks)

The current in the circuit increases as external resistance decreases (from I = ε / (R + r)).
The internal resistance causes a voltage drop (lost volts) equal to Ir.
As current increases, the voltage drop across the internal resistance (Ir) increases.
Since terminal pd = ε − Ir, a larger Ir means the terminal pd is smaller.

Key terms in this question

terminal potential difference