Under which condition the terminal potential difference across a battery and its emf are equal?
2 Answers
The terminal potential difference across a battery and its electromotive force (emf) are equal under the condition when there is no current flowing through the battery.
Let's break this down:
1. **Understanding emf and Terminal Potential Difference**:
- **Emf (Electromotive Force)**: This is the maximum potential difference between the terminals of a battery when no current is flowing. It represents the energy provided by the battery per unit charge.
- **Terminal Potential Difference**: This is the potential difference between the battery terminals when a current is flowing. It can be different from the emf due to internal resistance within the battery.
2. **Internal Resistance**:
- Batteries have internal resistance which causes a drop in potential difference when current flows. The terminal potential difference \( V_{\text{terminal}} \) can be expressed as:
\[
V_{\text{terminal}} = \text{emf} - I \cdot R_{\text{internal}}
\]
where \( I \) is the current and \( R_{\text{internal}} \) is the internal resistance of the battery.
3. **Condition for Equality**:
- When no current is flowing through the battery (i.e., the circuit is open or the battery is not connected to any load), the current \( I \) is zero.
- Under this condition:
\[
V_{\text{terminal}} = \text{emf} - (0 \cdot R_{\text{internal}}) = \text{emf}
\]
- Therefore, with no current, the potential difference across the terminals of the battery is equal to its emf.
In summary, the terminal potential difference equals the emf of the battery when there is no current flowing through the battery.
Let's break this down:
1. **Understanding emf and Terminal Potential Difference**:
- **Emf (Electromotive Force)**: This is the maximum potential difference between the terminals of a battery when no current is flowing. It represents the energy provided by the battery per unit charge.
- **Terminal Potential Difference**: This is the potential difference between the battery terminals when a current is flowing. It can be different from the emf due to internal resistance within the battery.
2. **Internal Resistance**:
- Batteries have internal resistance which causes a drop in potential difference when current flows. The terminal potential difference \( V_{\text{terminal}} \) can be expressed as:
\[
V_{\text{terminal}} = \text{emf} - I \cdot R_{\text{internal}}
\]
where \( I \) is the current and \( R_{\text{internal}} \) is the internal resistance of the battery.
3. **Condition for Equality**:
- When no current is flowing through the battery (i.e., the circuit is open or the battery is not connected to any load), the current \( I \) is zero.
- Under this condition:
\[
V_{\text{terminal}} = \text{emf} - (0 \cdot R_{\text{internal}}) = \text{emf}
\]
- Therefore, with no current, the potential difference across the terminals of the battery is equal to its emf.
In summary, the terminal potential difference equals the emf of the battery when there is no current flowing through the battery.
The terminal potential difference across a battery is equal to its electromotive force (emf) under specific conditions. These conditions occur when the battery is not supplying any current to an external circuit. This typically happens when:
1. **The battery is in an open circuit** (i.e., no current flows through it).
2. **The internal resistance of the battery has no impact** (as no current is flowing to generate a voltage drop across the internal resistance).
### Explanation:
A battery has two important characteristics:
- **Electromotive force (emf)**: This is the maximum voltage the battery can provide when no current flows through the circuit. It represents the energy supplied by the battery per unit charge.
- **Terminal potential difference (V)**: This is the actual voltage across the terminals of the battery when current flows in the circuit. The terminal voltage may differ from the emf due to the battery's internal resistance.
The relationship between emf (ε), terminal potential difference (V), internal resistance (r), and current (I) is described by the formula:
\[
V = \varepsilon - I \cdot r
\]
Where:
- \( \varepsilon \) = emf of the battery
- \( V \) = terminal potential difference
- \( I \) = current flowing through the circuit
- \( r \) = internal resistance of the battery
### Conditions for Terminal Potential Difference to Equal emf:
For \( V = \varepsilon \), the current \( I \) must be zero. This happens in two cases:
1. **No current (open circuit condition):** When the battery is not connected to any external load, the current \( I = 0 \). Since \( I \cdot r = 0 \), the terminal potential difference equals the emf, i.e., \( V = \varepsilon \).
2. **Ideal battery (no internal resistance):** If the battery had no internal resistance (which is ideal but not practical), there would be no voltage drop across the internal resistance, so \( V = \varepsilon \) even when current flows.
In summary, the terminal potential difference across a battery is equal to its emf only when the battery is not supplying current (open circuit) or when the battery has no internal resistance (ideal case).
1. **The battery is in an open circuit** (i.e., no current flows through it).
2. **The internal resistance of the battery has no impact** (as no current is flowing to generate a voltage drop across the internal resistance).
### Explanation:
A battery has two important characteristics:
- **Electromotive force (emf)**: This is the maximum voltage the battery can provide when no current flows through the circuit. It represents the energy supplied by the battery per unit charge.
- **Terminal potential difference (V)**: This is the actual voltage across the terminals of the battery when current flows in the circuit. The terminal voltage may differ from the emf due to the battery's internal resistance.
The relationship between emf (ε), terminal potential difference (V), internal resistance (r), and current (I) is described by the formula:
\[
V = \varepsilon - I \cdot r
\]
Where:
- \( \varepsilon \) = emf of the battery
- \( V \) = terminal potential difference
- \( I \) = current flowing through the circuit
- \( r \) = internal resistance of the battery
### Conditions for Terminal Potential Difference to Equal emf:
For \( V = \varepsilon \), the current \( I \) must be zero. This happens in two cases:
1. **No current (open circuit condition):** When the battery is not connected to any external load, the current \( I = 0 \). Since \( I \cdot r = 0 \), the terminal potential difference equals the emf, i.e., \( V = \varepsilon \).
2. **Ideal battery (no internal resistance):** If the battery had no internal resistance (which is ideal but not practical), there would be no voltage drop across the internal resistance, so \( V = \varepsilon \) even when current flows.
In summary, the terminal potential difference across a battery is equal to its emf only when the battery is not supplying current (open circuit) or when the battery has no internal resistance (ideal case).