Question

When the emf of the battery is equal to its terminal potential difference?

Answer 1

The electromotive force (emf) of a battery is defined as the potential difference across the terminals of the battery when no current is flowing, whereas the terminal potential difference is the voltage measured across the terminals of the battery when it is under load (i.e., when current is flowing).

The emf of a battery is equal to its terminal potential difference in the following conditions:

1. **No Load Condition**: When the battery is not supplying any current (open-circuit condition), the emf equals the terminal potential difference. This is because there are no voltage drops due to internal resistance.

2. **Ideal Conditions**: In an ideal battery (which has no internal resistance), the emf will always equal the terminal potential difference, regardless of the load.

3. **Zero Current**: If the current flowing through the circuit is zero (e.g., a switch is open), then the terminal voltage is equal to the emf.

When the battery is supplying current, the terminal potential difference will be less than the emf due to the voltage drop across the internal resistance of the battery, which can be described by the equation:

\[
V = \text{emf} - I \cdot r
\]

where:
- \(V\) is the terminal potential difference,
- \(I\) is the current flowing through the circuit,
- \(r\) is the internal resistance of the battery.

In summary, the emf of a battery is equal to its terminal potential difference only when there is no current flowing or in ideal conditions without internal resistance.

Answer 2

The electromotive force (EMF) of a battery is equal to its terminal potential difference when the battery is not supplying any current to an external circuit. This condition occurs when the battery is in an open circuit, meaning that no current is flowing through the circuit.

Here's why this happens:

1. **Definition of EMF**: The EMF of a battery is the maximum potential difference it can provide when no current is flowing. It represents the energy provided per unit charge by the battery.

2. **Terminal Potential Difference**: The terminal potential difference is the voltage measured across the terminals of the battery when it is connected to an external circuit.

3. **Internal Resistance**: A real battery has internal resistance, which causes a voltage drop inside the battery when current flows. This internal resistance causes the terminal potential difference to be less than the EMF when there is a current.

4. **Open Circuit Condition**: In an open circuit (where no current flows), there is no voltage drop across the internal resistance of the battery. Hence, the terminal potential difference equals the EMF of the battery.

In summary, the EMF of the battery equals the terminal potential difference when the battery is in an open circuit, meaning no current is flowing through the battery.