The terminals of a battery of emf 24.0 V and internal resistance of 1.0 Ω is connected to an external resistor 5.0 Ω. Find the terminal p.d.

Analyze the question: A battery with emf E = 24.0 V and internal resistance r = 1.0 Ω is connected to an external resistor R = 5.0 Ω. We need the terminal p.d., which is the voltage across the external resistor when current flows.

Concept:

• emf: E = I(R + r)
• Terminal p.d.: V = E − Ir = IR

Solution:

1. Total resistance = R + r = 5.0 + 1.0 = 6.0 Ω
2. Current: I = E / (R + r) = 24.0 / 6.0 = 4.0 A
3. Terminal p.d.: V = IR = 4.0 × 5.0 = 20.0 V

Check: V = E − Ir = 24 − (4.0 × 1.0) = 20 V ✓

Answer: The terminal p.d. is 20.0 V, which is option D.

Tip: Use the potential divider shortcut: V = E × R/(R + r) = 24 × 5/6 = 20 V. The terminal p.d. is always less than the emf when current flows, because some voltage ("lost volts", Ir) is dropped across the internal resistance.