Why terminal voltage is greater than emf when battery is charging or discharging?
2 Answers
When dealing with batteries, it's important to understand the concepts of electromotive force (emf) and terminal voltage. These terms describe different aspects of a battery's behavior, particularly in relation to its state of charge or discharge.
### Definitions
- **Electromotive Force (emf)**: This is the maximum potential difference a battery can provide when no current is flowing through the circuit. It's essentially the battery's inherent ability to push charge through the circuit, given its internal chemical reactions. Emf is a property of the battery itself and is determined by the chemistry of the battery.
- **Terminal Voltage**: This is the voltage you measure across the terminals of the battery when it is connected to a circuit and current is flowing. It is the actual voltage available to the external circuit.
### Charging and Discharging States
1. **Battery Discharging**: When a battery is discharging, current flows from the battery to the external circuit. Inside the battery, there is an internal resistance that causes a voltage drop due to this current.
- **Voltage Drop Due to Internal Resistance**: The internal resistance of the battery causes a reduction in the terminal voltage compared to the emf. The terminal voltage \( V_{terminal} \) can be expressed as:
\[
V_{terminal} = \text{emf} - I \cdot R_{internal}
\]
where \( I \) is the current flowing through the circuit and \( R_{internal} \) is the internal resistance of the battery. As current flows, the product \( I \cdot R_{internal} \) represents the voltage drop across the internal resistance, reducing the terminal voltage.
2. **Battery Charging**: When a battery is being charged, the situation is different. The external power source is pushing current into the battery, and the battery's terminals are at a higher potential than its emf to overcome the internal resistance and to drive current into the battery.
- **Increased Terminal Voltage**: During charging, the terminal voltage \( V_{terminal} \) is actually higher than the emf because the external charger needs to apply a voltage greater than the battery’s emf to push current into the battery and overcome the internal resistance. The relationship in this case can be described as:
\[
V_{terminal} = \text{emf} + I \cdot R_{internal}
\]
Here, \( I \) is the charging current, and \( R_{internal} \) is again the internal resistance. The charger needs to provide a voltage that is greater than the battery’s emf to drive current into the battery and effectively overcome the internal resistance.
### Summary
- **Discharging**: Terminal voltage is lower than the emf because of the internal resistance causing a voltage drop.
- **Charging**: Terminal voltage is higher than the emf because the charger has to supply a voltage greater than the emf to drive current into the battery and overcome internal resistance.
Understanding these concepts helps in designing and managing battery systems, ensuring they operate efficiently and safely whether they're being charged or discharged.
### Definitions
- **Electromotive Force (emf)**: This is the maximum potential difference a battery can provide when no current is flowing through the circuit. It's essentially the battery's inherent ability to push charge through the circuit, given its internal chemical reactions. Emf is a property of the battery itself and is determined by the chemistry of the battery.
- **Terminal Voltage**: This is the voltage you measure across the terminals of the battery when it is connected to a circuit and current is flowing. It is the actual voltage available to the external circuit.
### Charging and Discharging States
1. **Battery Discharging**: When a battery is discharging, current flows from the battery to the external circuit. Inside the battery, there is an internal resistance that causes a voltage drop due to this current.
- **Voltage Drop Due to Internal Resistance**: The internal resistance of the battery causes a reduction in the terminal voltage compared to the emf. The terminal voltage \( V_{terminal} \) can be expressed as:
\[
V_{terminal} = \text{emf} - I \cdot R_{internal}
\]
where \( I \) is the current flowing through the circuit and \( R_{internal} \) is the internal resistance of the battery. As current flows, the product \( I \cdot R_{internal} \) represents the voltage drop across the internal resistance, reducing the terminal voltage.
2. **Battery Charging**: When a battery is being charged, the situation is different. The external power source is pushing current into the battery, and the battery's terminals are at a higher potential than its emf to overcome the internal resistance and to drive current into the battery.
- **Increased Terminal Voltage**: During charging, the terminal voltage \( V_{terminal} \) is actually higher than the emf because the external charger needs to apply a voltage greater than the battery’s emf to push current into the battery and overcome the internal resistance. The relationship in this case can be described as:
\[
V_{terminal} = \text{emf} + I \cdot R_{internal}
\]
Here, \( I \) is the charging current, and \( R_{internal} \) is again the internal resistance. The charger needs to provide a voltage that is greater than the battery’s emf to drive current into the battery and effectively overcome the internal resistance.
### Summary
- **Discharging**: Terminal voltage is lower than the emf because of the internal resistance causing a voltage drop.
- **Charging**: Terminal voltage is higher than the emf because the charger has to supply a voltage greater than the emf to drive current into the battery and overcome internal resistance.
Understanding these concepts helps in designing and managing battery systems, ensuring they operate efficiently and safely whether they're being charged or discharged.
The terminal voltage of a battery can be greater or less than its electromotive force (EMF) depending on whether the battery is charging or discharging. This behavior is due to the internal resistance of the battery and the associated voltage drops or gains. Here’s a detailed explanation:
### Key Concepts
1. **EMF (Electromotive Force)**: This is the maximum potential difference between the terminals of the battery when no current is flowing. It represents the energy provided by the battery per unit charge.
2. **Terminal Voltage**: This is the actual voltage across the terminals of the battery when it is connected to a circuit and current is flowing.
3. **Internal Resistance**: All real batteries have some internal resistance, denoted as \( r \). This resistance causes a voltage drop inside the battery when current flows through it.
### Charging a Battery
When a battery is being charged:
- **Charging Current Direction**: Current flows into the battery, reversing the usual direction of current flow compared to discharging.
- **Voltage Behavior**: The terminal voltage of the battery is **greater than** its EMF. This is because the charger supplies a voltage that is higher than the battery's EMF to overcome both the EMF of the battery and the internal resistance.
- **Equation**: The terminal voltage \( V_T \) can be expressed as:
\[
V_T = \text{EMF} + I \cdot r
\]
where \( I \) is the charging current and \( r \) is the internal resistance. Since the charger must provide a voltage greater than the battery's EMF to push current into the battery, the terminal voltage during charging is higher than the EMF.
### Discharging a Battery
When a battery is discharging:
- **Discharging Current Direction**: Current flows out of the battery to the external circuit.
- **Voltage Behavior**: The terminal voltage of the battery is **less than** its EMF. This is because the internal resistance of the battery causes a voltage drop that reduces the voltage available across the terminals.
- **Equation**: The terminal voltage \( V_T \) can be expressed as:
\[
V_T = \text{EMF} - I \cdot r
\]
where \( I \) is the discharging current and \( r \) is the internal resistance. As current flows through the battery, the internal resistance causes a voltage drop, so the terminal voltage is lower than the EMF.
### Summary
- **Charging**: Terminal Voltage > EMF (since charging current causes a voltage increase across internal resistance).
- **Discharging**: Terminal Voltage < EMF (since discharging current causes a voltage drop across internal resistance).
Understanding these concepts is crucial for applications that involve battery operation, such as in electrical circuits, energy storage systems, and electronic devices.
### Key Concepts
1. **EMF (Electromotive Force)**: This is the maximum potential difference between the terminals of the battery when no current is flowing. It represents the energy provided by the battery per unit charge.
2. **Terminal Voltage**: This is the actual voltage across the terminals of the battery when it is connected to a circuit and current is flowing.
3. **Internal Resistance**: All real batteries have some internal resistance, denoted as \( r \). This resistance causes a voltage drop inside the battery when current flows through it.
### Charging a Battery
When a battery is being charged:
- **Charging Current Direction**: Current flows into the battery, reversing the usual direction of current flow compared to discharging.
- **Voltage Behavior**: The terminal voltage of the battery is **greater than** its EMF. This is because the charger supplies a voltage that is higher than the battery's EMF to overcome both the EMF of the battery and the internal resistance.
- **Equation**: The terminal voltage \( V_T \) can be expressed as:
\[
V_T = \text{EMF} + I \cdot r
\]
where \( I \) is the charging current and \( r \) is the internal resistance. Since the charger must provide a voltage greater than the battery's EMF to push current into the battery, the terminal voltage during charging is higher than the EMF.
### Discharging a Battery
When a battery is discharging:
- **Discharging Current Direction**: Current flows out of the battery to the external circuit.
- **Voltage Behavior**: The terminal voltage of the battery is **less than** its EMF. This is because the internal resistance of the battery causes a voltage drop that reduces the voltage available across the terminals.
- **Equation**: The terminal voltage \( V_T \) can be expressed as:
\[
V_T = \text{EMF} - I \cdot r
\]
where \( I \) is the discharging current and \( r \) is the internal resistance. As current flows through the battery, the internal resistance causes a voltage drop, so the terminal voltage is lower than the EMF.
### Summary
- **Charging**: Terminal Voltage > EMF (since charging current causes a voltage increase across internal resistance).
- **Discharging**: Terminal Voltage < EMF (since discharging current causes a voltage drop across internal resistance).
Understanding these concepts is crucial for applications that involve battery operation, such as in electrical circuits, energy storage systems, and electronic devices.