Explain why the terminal potential difference of a battery decreases when the current drawn from the battery increases.

IB DP Physics Standard 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 has an electromotive force (EMF) of 9.0 V and a fixed internal resistance. When the battery is connected to an external circuit, the measured terminal potential difference is found to be less than 9.0 V, and this difference becomes larger as more current is drawn.

Model answer (4 marks)

The EMF of the battery is the open‑circuit potential difference (9.0 V). When a load is connected a current I flows through the internal resistance r, creating a voltage drop Ir. The terminal potential difference is therefore V_terminal = EMF – Ir. As the current drawn increases, the drop Ir increases, so V_terminal decreases.

Examiner tips

Use the formula V_terminal = EMF – Ir to link EMF, internal resistance and terminal voltage.
Show the relationship between increasing I and increasing Ir, leading to a lower terminal voltage.
Mention that the EMF remains constant while the internal drop changes.
Keep the explanation concise and use the exact terms from the mark scheme.

Common mistakes

Confusing EMF with terminal voltage; stating that EMF decreases. Mis‑applying Ohm’s law to the external circuit instead of the internal resistance. Forgetting to include the minus sign in V_terminal = EMF – Ir.

Mark scheme (4 marks)

EMF is the total energy supplied per unit charge by the battery (or: the open-circuit potential difference across the battery terminals).
The battery has an internal resistance, so when current flows there is a potential difference (voltage drop) across the internal resistance.
The terminal potential difference equals EMF minus the voltage drop across the internal resistance (terminal pd = EMF − Ir).
As current increases, the voltage drop across the internal resistance (Ir) increases, so the terminal potential difference decreases further.

Key terms in this question

terminal potential difference