Can potential difference across the terminals of a battery be greater than its emf?
2 Answers
Yes, the potential difference (voltage) across the terminals of a battery can be greater than its electromotive force (emf), but this can only occur under certain conditions.
### Key Concepts:
1. **EMF (Electromotive Force):**
- The emf of a battery is the maximum potential difference between the two terminals of the battery when no current is flowing, i.e., when the circuit is open. It represents the energy supplied by the battery per unit charge and is determined by the chemical composition of the battery.
- EMF is the "ideal" voltage of the battery and is constant for a given battery under standard conditions.
2. **Potential Difference (Terminal Voltage):**
- The potential difference across the terminals of a battery, also known as terminal voltage, is the actual voltage you measure across the battery when it is connected in a circuit and supplying current.
- Terminal voltage depends on both the internal resistance of the battery and the current flowing through the circuit.
### When is the Potential Difference Greater than the EMF?
This situation can occur during a process called **charging the battery**. Here’s why:
- **During Discharge (Normal Operation):**
When the battery is supplying power to an external load, the terminal voltage is typically *less* than the emf because of the **internal resistance** of the battery. This internal resistance causes a voltage drop when current flows, and the terminal voltage \( V \) is given by:
\[
V = \text{EMF} - I \cdot r
\]
where:
- \( V \) = terminal voltage
- \( I \) = current drawn by the load
- \( r \) = internal resistance of the battery
- EMF = electromotive force (constant for the battery)
This means that when current is flowing, the terminal voltage drops below the emf due to the loss inside the battery.
- **During Charging:**
When you charge the battery, current is forced into it in the reverse direction. In this case, the potential difference across the terminals can exceed the emf because you are pushing energy into the battery. The terminal voltage in this case is given by:
\[
V = \text{EMF} + I \cdot r
\]
This equation shows that the terminal voltage is greater than the emf during charging because of the internal resistance. The external charger applies a voltage greater than the emf to drive current into the battery, overcoming both the emf and the voltage drop due to internal resistance.
### Summary:
- **Discharging Battery:** Terminal voltage \( V \) is less than the emf due to the internal resistance and voltage drop as current flows.
- **Charging Battery:** Terminal voltage \( V \) can be greater than the emf because external energy is pushing current in, overcoming internal resistance and the battery's emf.
Thus, under charging conditions, the potential difference across the battery terminals can exceed the emf.
### Key Concepts:
1. **EMF (Electromotive Force):**
- The emf of a battery is the maximum potential difference between the two terminals of the battery when no current is flowing, i.e., when the circuit is open. It represents the energy supplied by the battery per unit charge and is determined by the chemical composition of the battery.
- EMF is the "ideal" voltage of the battery and is constant for a given battery under standard conditions.
2. **Potential Difference (Terminal Voltage):**
- The potential difference across the terminals of a battery, also known as terminal voltage, is the actual voltage you measure across the battery when it is connected in a circuit and supplying current.
- Terminal voltage depends on both the internal resistance of the battery and the current flowing through the circuit.
### When is the Potential Difference Greater than the EMF?
This situation can occur during a process called **charging the battery**. Here’s why:
- **During Discharge (Normal Operation):**
When the battery is supplying power to an external load, the terminal voltage is typically *less* than the emf because of the **internal resistance** of the battery. This internal resistance causes a voltage drop when current flows, and the terminal voltage \( V \) is given by:
\[
V = \text{EMF} - I \cdot r
\]
where:
- \( V \) = terminal voltage
- \( I \) = current drawn by the load
- \( r \) = internal resistance of the battery
- EMF = electromotive force (constant for the battery)
This means that when current is flowing, the terminal voltage drops below the emf due to the loss inside the battery.
- **During Charging:**
When you charge the battery, current is forced into it in the reverse direction. In this case, the potential difference across the terminals can exceed the emf because you are pushing energy into the battery. The terminal voltage in this case is given by:
\[
V = \text{EMF} + I \cdot r
\]
This equation shows that the terminal voltage is greater than the emf during charging because of the internal resistance. The external charger applies a voltage greater than the emf to drive current into the battery, overcoming both the emf and the voltage drop due to internal resistance.
### Summary:
- **Discharging Battery:** Terminal voltage \( V \) is less than the emf due to the internal resistance and voltage drop as current flows.
- **Charging Battery:** Terminal voltage \( V \) can be greater than the emf because external energy is pushing current in, overcoming internal resistance and the battery's emf.
Thus, under charging conditions, the potential difference across the battery terminals can exceed the emf.
No, the potential difference across the terminals of a battery cannot be greater than its electromotive force (EMF) when the battery is in a closed circuit. Here’s a detailed explanation:
### Understanding EMF and Terminal Potential Difference
1. **Electromotive Force (EMF):**
- The EMF of a battery is the maximum potential difference it can provide when no current is flowing through it. It represents the work done per unit charge by the battery to move charge from one terminal to the other inside the battery.
- EMF is a characteristic of the battery and is determined by its chemical composition and construction.
2. **Terminal Potential Difference (V):**
- The terminal potential difference is the voltage measured across the terminals of the battery when it is connected in a circuit and current is flowing.
- This potential difference is equal to the EMF minus the internal voltage drop caused by the internal resistance of the battery.
### Relationship Between EMF and Terminal Potential Difference
In a circuit, when a battery is supplying current, the terminal potential difference \( V \) is less than the EMF \( \mathcal{E} \) due to the internal resistance \( r \) of the battery. The relationship can be expressed as:
\[ V = \mathcal{E} - I \cdot r \]
where:
- \( I \) is the current flowing through the circuit.
- \( r \) is the internal resistance of the battery.
**Key Points:**
1. **No Current Case:**
- When the battery is not connected to a circuit (i.e., no current flows), the terminal potential difference equals the EMF of the battery.
2. **With Current Flowing:**
- When current flows, the internal resistance causes a voltage drop inside the battery. As a result, the terminal potential difference \( V \) is always less than the EMF.
3. **Internal Resistance Impact:**
- The internal resistance \( r \) of the battery always causes some loss of voltage. Thus, \( \mathcal{E} > V \) when current flows.
4. **In Ideal Conditions:**
- An ideal battery with no internal resistance would have the terminal potential difference equal to the EMF for all operating conditions.
### Special Cases
1. **Reversed Polarity:**
- If the battery is reversed in a circuit (with respect to its polarity), the terminal potential difference can be negative relative to the EMF.
2. **Open Circuit:**
- In an open circuit, where no current flows, the terminal potential difference is equal to the EMF.
In summary, the terminal potential difference across the terminals of a battery can never exceed its EMF when the battery is in use and current is flowing through the circuit.
### Understanding EMF and Terminal Potential Difference
1. **Electromotive Force (EMF):**
- The EMF of a battery is the maximum potential difference it can provide when no current is flowing through it. It represents the work done per unit charge by the battery to move charge from one terminal to the other inside the battery.
- EMF is a characteristic of the battery and is determined by its chemical composition and construction.
2. **Terminal Potential Difference (V):**
- The terminal potential difference is the voltage measured across the terminals of the battery when it is connected in a circuit and current is flowing.
- This potential difference is equal to the EMF minus the internal voltage drop caused by the internal resistance of the battery.
### Relationship Between EMF and Terminal Potential Difference
In a circuit, when a battery is supplying current, the terminal potential difference \( V \) is less than the EMF \( \mathcal{E} \) due to the internal resistance \( r \) of the battery. The relationship can be expressed as:
\[ V = \mathcal{E} - I \cdot r \]
where:
- \( I \) is the current flowing through the circuit.
- \( r \) is the internal resistance of the battery.
**Key Points:**
1. **No Current Case:**
- When the battery is not connected to a circuit (i.e., no current flows), the terminal potential difference equals the EMF of the battery.
2. **With Current Flowing:**
- When current flows, the internal resistance causes a voltage drop inside the battery. As a result, the terminal potential difference \( V \) is always less than the EMF.
3. **Internal Resistance Impact:**
- The internal resistance \( r \) of the battery always causes some loss of voltage. Thus, \( \mathcal{E} > V \) when current flows.
4. **In Ideal Conditions:**
- An ideal battery with no internal resistance would have the terminal potential difference equal to the EMF for all operating conditions.
### Special Cases
1. **Reversed Polarity:**
- If the battery is reversed in a circuit (with respect to its polarity), the terminal potential difference can be negative relative to the EMF.
2. **Open Circuit:**
- In an open circuit, where no current flows, the terminal potential difference is equal to the EMF.
In summary, the terminal potential difference across the terminals of a battery can never exceed its EMF when the battery is in use and current is flowing through the circuit.