The emf of a cell is the potential difference across its terminals when it is in

1. Analyze the Question

The question asks for the specific condition under which the potential difference across the terminals of a cell is equal to its electromotive force (emf).

2. Explain the Concept

• Electromotive Force (emf): This is the total energy supplied by a cell per unit charge to drive current around a complete circuit. It is the voltage of the cell when no current is flowing.
• Terminal Potential Difference (V): This is the voltage measured across the terminals of a cell when current is flowing through an external circuit.
• The Relationship: The relationship is given by the formula: $$V = E - Ir$$ Where: • $E$ = emf • $I$ = current flowing through the circuit • $r$ = internal resistance of the cell

When the circuit is open, no current flows ($I = 0$). Substituting this into the formula:

3. Show the Solution

• In a closed circuit (Option B), current flows, and the terminal voltage is always less than the emf due to the "lost volts" ($Ir$) across the internal resistance.
• In an open circuit (Option C), the circuit is broken, meaning no current can flow. Because there is no current, there is no voltage drop across the internal resistance. Therefore, the potential difference measured across the terminals is exactly equal to the emf of the cell.

4. Identify the Answer

The correct condition is an open circuit.

Correct Option: C

5. Exam Tip

Think of emf as the "maximum potential" a battery can provide. As soon as you connect it to a bulb or device (closing the circuit), the battery has to work against its own internal resistance, which "steals" some of that potential. Therefore, you only see the full emf when the battery is "resting" in an open circuit!