A cell of e.m.f 12V and internal resistance 4Ω is connected to an external resistor of resistance 2Ω. Find the current flow.

Analyze the question We have a cell with e.m.f. E = 12 V and internal resistance r = 4 Ω, connected to an external resistor R = 2 Ω. We need the current in the circuit.

Concept The e.m.f. drives current through the total resistance of the circuit, which is the external resistance plus the internal resistance:

E = I(R + r), so I = E / (R + r)

Solution

1. Total resistance = R + r = 2 + 4 = 6 Ω
2. Current: I = 12 / 6 = 2 A

Check:

• Voltage lost inside the cell = Ir = 2 × 4 = 8 V
• Terminal voltage across the resistor = IR = 2 × 2 = 4 V
• 8 V + 4 V = 12 V, which matches the e.m.f.

Answer: The current is 2 A, which is option D.

Exam tip: Many students forget the internal resistance and calculate 12 / 2 = 6 A, which is not even an option here. Always add r to R first. Remember the formula E = I(R + r), or "e.m.f. = terminal voltage + lost volts".