Question

Under what condition the terminal potential difference across a battery and emf are equal?

Answer 1

The terminal potential difference across a battery and its electromotive force (EMF) are equal under the condition of **no current flowing through the battery**. This occurs in an open-circuit situation where the circuit is not closed, so no current is drawn from the battery.

Here’s a more detailed explanation:

- **EMF (Electromotive Force):** This is the maximum potential difference that a battery can provide when no current is flowing. It represents the energy supplied per unit charge by the battery’s internal chemical reactions.

- **Terminal Potential Difference:** This is the actual potential difference measured across the battery terminals when the battery is connected in a circuit.

When no current is flowing (open circuit):
- There is no voltage drop across the internal resistance of the battery because the internal resistance \( r \) times the current \( I \) (which is zero in this case) is zero (\( V_{drop} = I \cdot r = 0 \)).
- Therefore, the terminal potential difference \( V_{terminal} \) is equal to the EMF of the battery (\( \mathcal{E} \)).

In summary, when the battery is not supplying any current (open circuit), the terminal potential difference is equal to the EMF.

Answer 2

The terminal potential difference across a battery and its electromotive force (emf) are equal under the following condition:

**When no current is flowing through the battery.**

This condition occurs in an open circuit, meaning that the battery is not connected to any load or external circuit, so there is no current flowing. In this state, the terminal potential difference (V) equals the emf (E) of the battery because the voltage drop due to internal resistance is zero.

In a closed circuit with current flowing, the terminal potential difference will be less than the emf due to the voltage drop across the internal resistance of the battery.