Question

Is potential difference across the terminals of a battery always less than the emf of the battery?

Answer 1

To understand the relationship between the potential difference (or terminal voltage) across the terminals of a battery and its electromotive force (emf), we need to consider the concepts of emf, internal resistance, and circuit behavior.

### Definitions:
1. **Emf (Electromotive Force)**: This is the maximum potential difference the battery can provide when no current is flowing. It is essentially the energy provided per unit charge by the battery's chemical reaction.
  
2. **Potential Difference (Terminal Voltage)**: This is the voltage measured across the battery’s terminals when it is connected to a circuit and current is flowing. It reflects the actual voltage available for use in the circuit.

### Internal Resistance:
Batteries have some internal resistance (denoted as \( r \)). This resistance causes a drop in voltage when current flows through the battery. The relationship can be described with the following equation:

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

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

### When is the Terminal Voltage Less than Emf?
- **No Current Flowing**: If the battery is not connected to any load (open circuit), the current \( I = 0 \). In this case, the terminal voltage equals the emf:
  \[
  V = \text{emf}
  \]

- **Current Flowing**: When the battery is connected to a load (closed circuit) and current flows, the terminal voltage will generally be less than the emf due to the voltage drop across the internal resistance:
  \[
  V < \text{emf}
  \]

### Special Cases:
1. **Short-Circuit Condition**: If the terminals of the battery are connected directly with a wire (a short circuit), the potential difference will drop significantly, approaching zero. In this extreme case, the terminal voltage is much less than the emf.

2. **High Internal Resistance**: In batteries with a high internal resistance or under heavy load conditions, the terminal voltage can drop significantly below the emf.

### Conclusion:
In summary, the potential difference across the terminals of a battery is **always equal to the emf when no current is flowing**. However, when current is drawn from the battery, the terminal voltage is usually **less than the emf** due to the internal resistance. This drop can vary depending on the current being drawn and the internal characteristics of the battery.

Answer 2

Yes, the potential difference (or voltage) across the terminals of a battery is typically less than its electromotive force (EMF). The EMF of a battery is the maximum potential difference the battery can provide when no current is flowing.

However, when a current flows through the battery, there is a voltage drop due to the internal resistance of the battery. This drop means that the potential difference across the battery terminals will be less than the EMF. The relationship can be expressed as:

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

where:
- \( V \) is the terminal voltage.
- \(\text{EMF}\) is the electromotive force.
- \( I \) is the current flowing through the battery.
- \( r \) is the internal resistance of the battery.

So, if there is any current flowing, the terminal voltage will always be less than the EMF of the battery.