Under what condition the terminal potential difference is greater than the emf of battery?
2 Answers
The terminal potential difference (V) can be greater than the electromotive force (emf, \( \mathcal{E} \)) of a battery under certain conditions involving external influences. Here are two scenarios where this can happen:
1. **In a Discharging Capacitor in Series with the Battery:**
If a capacitor is in series with a battery and is initially charged, the terminal potential difference across the battery can exceed the emf of the battery. This is because the capacitor can provide a potential difference that adds to the emf of the battery. For example, if a charged capacitor with voltage \( V_C \) is connected in series with a battery of emf \( \mathcal{E} \), the total voltage across the combination can be \( V_C + \mathcal{E} \) if the capacitor is discharging.
2. **In a Circuit with Inductive Kickback:**
If an inductive load (like a coil) in a circuit is suddenly disconnected or switched off, the collapsing magnetic field can induce a high voltage across the inductive load. This phenomenon is known as inductive kickback. If this induced voltage is in the same direction as the battery's emf, the total potential difference across the terminals of the battery can be greater than the emf of the battery alone.
In both scenarios, the potential difference is influenced by additional factors beyond the emf of the battery.
1. **In a Discharging Capacitor in Series with the Battery:**
If a capacitor is in series with a battery and is initially charged, the terminal potential difference across the battery can exceed the emf of the battery. This is because the capacitor can provide a potential difference that adds to the emf of the battery. For example, if a charged capacitor with voltage \( V_C \) is connected in series with a battery of emf \( \mathcal{E} \), the total voltage across the combination can be \( V_C + \mathcal{E} \) if the capacitor is discharging.
2. **In a Circuit with Inductive Kickback:**
If an inductive load (like a coil) in a circuit is suddenly disconnected or switched off, the collapsing magnetic field can induce a high voltage across the inductive load. This phenomenon is known as inductive kickback. If this induced voltage is in the same direction as the battery's emf, the total potential difference across the terminals of the battery can be greater than the emf of the battery alone.
In both scenarios, the potential difference is influenced by additional factors beyond the emf of the battery.
The terminal potential difference (V) of a battery can be greater than its electromotive force (EMF) under certain conditions, particularly when the battery is not delivering current to an external circuit but is instead in a special state of operation. Here’s a detailed explanation:
### Understanding EMF and Terminal Potential Difference
- **Electromotive Force (EMF):** This is the maximum potential difference that a battery can provide when no current is flowing through the circuit. It represents the total energy per unit charge that the battery can supply due to the chemical reactions occurring within it.
- **Terminal Potential Difference (V):** This is the voltage measured across the terminals of the battery when it is connected to an external circuit. It is affected by the internal resistance of the battery and the current flowing through it.
### Basic Relation
For a battery with EMF \( E \) and internal resistance \( r \), the terminal potential difference \( V \) when current \( I \) flows through an external circuit is given by:
\[ V = E - Ir \]
Here’s a breakdown of how different conditions affect this relationship:
1. **No Current Flowing (Open Circuit Condition):**
- When the battery is not connected to any external circuit (i.e., there is no current flowing), the terminal potential difference is equal to the EMF of the battery:
\[ V = E \]
- There is no voltage drop across the internal resistance \( r \) because \( I = 0 \).
2. **Charging the Battery:**
- When a battery is being charged, an external power source applies a voltage to the battery that is higher than its EMF. In this case, the terminal potential difference can temporarily exceed the battery's EMF.
- The relationship during charging can be expressed as:
\[ V_{\text{charging}} = E + I_{\text{charging}} \times r \]
- Here, \( I_{\text{charging}} \) is the current supplied by the external power source. The terminal potential difference during charging is therefore:
\[ V_{\text{charging}} > E \]
- This increase occurs because the external power source is supplying additional voltage to overcome the EMF and charge the battery.
3. **Measurement Errors or Special Conditions:**
- In practical scenarios, there could be measurement errors or unique conditions that might momentarily show a terminal voltage higher than the EMF, but these are generally not typical or stable conditions.
### Summary
Under normal conditions, the terminal potential difference of a battery is generally less than or equal to its EMF due to the internal resistance of the battery. However, when the battery is being charged, the terminal potential difference can exceed the EMF. This is because the external power source applies a higher voltage to force current into the battery, causing the terminal potential difference to rise above the battery’s EMF.
### Understanding EMF and Terminal Potential Difference
- **Electromotive Force (EMF):** This is the maximum potential difference that a battery can provide when no current is flowing through the circuit. It represents the total energy per unit charge that the battery can supply due to the chemical reactions occurring within it.
- **Terminal Potential Difference (V):** This is the voltage measured across the terminals of the battery when it is connected to an external circuit. It is affected by the internal resistance of the battery and the current flowing through it.
### Basic Relation
For a battery with EMF \( E \) and internal resistance \( r \), the terminal potential difference \( V \) when current \( I \) flows through an external circuit is given by:
\[ V = E - Ir \]
Here’s a breakdown of how different conditions affect this relationship:
1. **No Current Flowing (Open Circuit Condition):**
- When the battery is not connected to any external circuit (i.e., there is no current flowing), the terminal potential difference is equal to the EMF of the battery:
\[ V = E \]
- There is no voltage drop across the internal resistance \( r \) because \( I = 0 \).
2. **Charging the Battery:**
- When a battery is being charged, an external power source applies a voltage to the battery that is higher than its EMF. In this case, the terminal potential difference can temporarily exceed the battery's EMF.
- The relationship during charging can be expressed as:
\[ V_{\text{charging}} = E + I_{\text{charging}} \times r \]
- Here, \( I_{\text{charging}} \) is the current supplied by the external power source. The terminal potential difference during charging is therefore:
\[ V_{\text{charging}} > E \]
- This increase occurs because the external power source is supplying additional voltage to overcome the EMF and charge the battery.
3. **Measurement Errors or Special Conditions:**
- In practical scenarios, there could be measurement errors or unique conditions that might momentarily show a terminal voltage higher than the EMF, but these are generally not typical or stable conditions.
### Summary
Under normal conditions, the terminal potential difference of a battery is generally less than or equal to its EMF due to the internal resistance of the battery. However, when the battery is being charged, the terminal potential difference can exceed the EMF. This is because the external power source applies a higher voltage to force current into the battery, causing the terminal potential difference to rise above the battery’s EMF.