Why is the terminal voltage across a battery more than the emf during charging?
2 Answers
The terminal voltage across a battery during charging can be more than its electromotive force (EMF) due to the interplay between the battery's internal resistance and the charging current. Let’s break this down step-by-step:
1. **Understanding EMF and Terminal Voltage:**
- **EMF (Electromotive Force):** This is the maximum potential difference the battery can provide when there is no current flowing through it. It's a measure of the battery's ability to drive current through an external circuit.
- **Terminal Voltage:** This is the actual voltage measured across the battery's terminals when it is connected to a circuit and current is flowing.
2. **Battery During Charging:**
- When a battery is being charged, a charging current is supplied by an external power source, such as a charger.
- The charging current flows through the battery and the battery’s internal resistance.
3. **Internal Resistance Effect:**
- **Internal Resistance:** This is the resistance within the battery that opposes the flow of current. It causes a voltage drop when current flows through it.
- The internal resistance leads to a voltage drop within the battery, which is given by Ohm's Law: \( V_{\text{drop}} = I \times R_{\text{internal}} \), where \( I \) is the charging current and \( R_{\text{internal}} \) is the internal resistance.
4. **Voltage Drop and Charging Voltage:**
- When charging, the terminal voltage (\( V_{\text{terminal}} \)) is higher than the EMF (\( E \)) of the battery. This happens because the charging voltage from the external power source must overcome both the battery's EMF and the voltage drop across its internal resistance.
- The external power source provides a voltage \( V_{\text{charging}} \) that is higher than the battery’s EMF by an amount equal to the internal resistance voltage drop. So, if the charging current is \( I \) and the internal resistance is \( R_{\text{internal}} \), the charging voltage must be \( V_{\text{charging}} = E + I \times R_{\text{internal}} \).
5. **Terminal Voltage During Charging:**
- As a result, during charging, the terminal voltage of the battery, which is the voltage you measure across its terminals, can be expressed as:
\[
V_{\text{terminal}} = E + I \times R_{\text{internal}}
\]
- This means that the terminal voltage is the sum of the battery’s EMF and the voltage drop due to the internal resistance. Since the charging voltage from the power source is typically set to be higher than the battery’s EMF to drive current into the battery, the terminal voltage can end up being higher than the EMF.
In summary, the terminal voltage across a battery during charging can be higher than the EMF due to the need to overcome both the battery's EMF and the voltage drop caused by its internal resistance. This allows the external power source to push current into the battery, leading to a higher observed terminal voltage.
1. **Understanding EMF and Terminal Voltage:**
- **EMF (Electromotive Force):** This is the maximum potential difference the battery can provide when there is no current flowing through it. It's a measure of the battery's ability to drive current through an external circuit.
- **Terminal Voltage:** This is the actual voltage measured across the battery's terminals when it is connected to a circuit and current is flowing.
2. **Battery During Charging:**
- When a battery is being charged, a charging current is supplied by an external power source, such as a charger.
- The charging current flows through the battery and the battery’s internal resistance.
3. **Internal Resistance Effect:**
- **Internal Resistance:** This is the resistance within the battery that opposes the flow of current. It causes a voltage drop when current flows through it.
- The internal resistance leads to a voltage drop within the battery, which is given by Ohm's Law: \( V_{\text{drop}} = I \times R_{\text{internal}} \), where \( I \) is the charging current and \( R_{\text{internal}} \) is the internal resistance.
4. **Voltage Drop and Charging Voltage:**
- When charging, the terminal voltage (\( V_{\text{terminal}} \)) is higher than the EMF (\( E \)) of the battery. This happens because the charging voltage from the external power source must overcome both the battery's EMF and the voltage drop across its internal resistance.
- The external power source provides a voltage \( V_{\text{charging}} \) that is higher than the battery’s EMF by an amount equal to the internal resistance voltage drop. So, if the charging current is \( I \) and the internal resistance is \( R_{\text{internal}} \), the charging voltage must be \( V_{\text{charging}} = E + I \times R_{\text{internal}} \).
5. **Terminal Voltage During Charging:**
- As a result, during charging, the terminal voltage of the battery, which is the voltage you measure across its terminals, can be expressed as:
\[
V_{\text{terminal}} = E + I \times R_{\text{internal}}
\]
- This means that the terminal voltage is the sum of the battery’s EMF and the voltage drop due to the internal resistance. Since the charging voltage from the power source is typically set to be higher than the battery’s EMF to drive current into the battery, the terminal voltage can end up being higher than the EMF.
In summary, the terminal voltage across a battery during charging can be higher than the EMF due to the need to overcome both the battery's EMF and the voltage drop caused by its internal resistance. This allows the external power source to push current into the battery, leading to a higher observed terminal voltage.