A cell of emf 1.5V is connected in series with a 1Ω resistor and a current of 0.3A flows through the resistor. Find the internal resistance of the cell

Analyze the question: A cell with emf E = 1.5 V drives a current I = 0.3 A through an external resistor R = 1 Ω. We need the internal resistance r.

Concept: The emf is shared between the external circuit and the cell's own internal resistance:

E = I(R + r)

Solution:

1. Total resistance = E / I = 1.5 / 0.3 = 5 Ω
2. External resistance R = 1 Ω
3. Internal resistance r = 5 − 1 = 4 Ω

Check: Lost volts = Ir = 0.3 × 4 = 1.2 V. Terminal voltage = IR = 0.3 × 1 = 0.3 V. Adding them: 1.2 + 0.3 = 1.5 V, which equals the emf. ✔

Answer: r = 4.0 Ω, which is option A.

Tip: For these questions, find the total resistance first (E ÷ I), then subtract the external resistance. Remember E = V + Ir, where V is the terminal voltage across the external resistor. If the current seems small for the emf given, the internal resistance is usually large.