A cell of emf 2 V has an internal resistance of 0.5 Ω. A current of 0.4 A passes through an external resistor, P. Determine the resistance of P.

Analyze the question: We have a cell with emf E = 2 V and internal resistance r = 0.5 Ω. The current is I = 0.4 A through external resistor P. We need R.

Concept: For a cell in a circuit,

E = I(R + r)

so R = E/I − r

Solution:

1. Total resistance of the circuit = E/I = 2 / 0.4 = 5 Ω
2. This total is R + r, so R = 5 − 0.5 = 4.5 Ω

Check: I = 2 / (4.5 + 0.5) = 2/5 = 0.4 A ✔

Answer: The resistance of P is 4.5 Ω, which is option A.

Common mistake: Option B (5 Ω) is the trap. It is the total resistance, and students forget to subtract the internal resistance.

Tip: Remember "E = V + Ir", or "emf = I × (total resistance)". Always ask yourself: is the resistance I found the total or just the external part? If the question asks for the external resistor, subtract r.