Under what condition is emf equal to terminal potential difference?
2 Answers
The electromotive force (emf) of a source is equal to the terminal potential difference when there is no current flowing through the circuit. This occurs when the circuit is open or when the load resistance is very high compared to the internal resistance of the source. In such cases, the voltage measured across the terminals reflects the full emf of the source, as there are no losses due to internal resistance.
When a current flows, the terminal potential difference drops below the emf due to the voltage drop across the internal resistance.
When a current flows, the terminal potential difference drops below the emf due to the voltage drop across the internal resistance.
The electromotive force (EMF) of a source and the terminal potential difference across the source are equal under the condition that there is no current flowing through the source.
Here's a detailed explanation:
1. **EMF Definition**: EMF is the maximum potential difference a source can provide when no current is flowing through it. It's essentially the work done per unit charge by the source when transferring charge from one terminal to another inside the source.
2. **Terminal Potential Difference**: The terminal potential difference is the actual voltage measured across the terminals of the source when it is connected in a circuit and current is flowing.
3. **Internal Resistance**: Real sources of EMF have internal resistance (denoted as \( r \)). When current \( I \) flows through the source, the terminal potential difference \( V_{terminal} \) is given by:
\[
V_{terminal} = \text{EMF} - I \cdot r
\]
Here, \( \text{EMF} \) is the EMF of the source, and \( r \) is the internal resistance of the source.
4. **Condition for Equality**:
- When no current flows (\( I = 0 \)), the term \( I \cdot r \) becomes zero.
- Hence, the terminal potential difference \( V_{terminal} \) is simply:
\[
V_{terminal} = \text{EMF}
\]
- Therefore, under no-load conditions or when the circuit is open (i.e., no current is flowing), the EMF is equal to the terminal potential difference.
In summary, the EMF is equal to the terminal potential difference when the circuit connected to the source is open, meaning no current is flowing through the circuit.
Here's a detailed explanation:
1. **EMF Definition**: EMF is the maximum potential difference a source can provide when no current is flowing through it. It's essentially the work done per unit charge by the source when transferring charge from one terminal to another inside the source.
2. **Terminal Potential Difference**: The terminal potential difference is the actual voltage measured across the terminals of the source when it is connected in a circuit and current is flowing.
3. **Internal Resistance**: Real sources of EMF have internal resistance (denoted as \( r \)). When current \( I \) flows through the source, the terminal potential difference \( V_{terminal} \) is given by:
\[
V_{terminal} = \text{EMF} - I \cdot r
\]
Here, \( \text{EMF} \) is the EMF of the source, and \( r \) is the internal resistance of the source.
4. **Condition for Equality**:
- When no current flows (\( I = 0 \)), the term \( I \cdot r \) becomes zero.
- Hence, the terminal potential difference \( V_{terminal} \) is simply:
\[
V_{terminal} = \text{EMF}
\]
- Therefore, under no-load conditions or when the circuit is open (i.e., no current is flowing), the EMF is equal to the terminal potential difference.
In summary, the EMF is equal to the terminal potential difference when the circuit connected to the source is open, meaning no current is flowing through the circuit.