Why is terminal voltage more than emf?
2 Answers
It seems like there might be a misunderstanding in the question. In most practical cases, the terminal voltage of a battery is actually less than its electromotive force (EMF), not more. Let’s break down why this is the case.
### Key Concepts
1. **Electromotive Force (EMF):** EMF is the maximum potential difference between the terminals of a battery when no current is flowing. It represents the battery’s ability to drive current through a circuit.
2. **Terminal Voltage:** Terminal voltage is the actual voltage available across the terminals of the battery when current is flowing. It is the voltage you measure when the battery is connected to a load and current is flowing through the circuit.
### Why Terminal Voltage is Less than EMF
When a battery is providing current to a circuit, the terminal voltage is affected by the internal resistance of the battery. Here’s how it works:
1. **Internal Resistance:** Every real battery has some internal resistance (denoted as \( r_{\text{int}} \)). This resistance causes a voltage drop inside the battery when current flows.
2. **Ohm’s Law and Voltage Drop:** According to Ohm’s Law, the voltage drop across the internal resistance of the battery is given by \( V_{\text{drop}} = I \cdot r_{\text{int}} \), where \( I \) is the current flowing through the circuit. This voltage drop occurs within the battery itself.
3. **Terminal Voltage Calculation:** The terminal voltage (\( V_{\text{term}} \)) can be found by subtracting the voltage drop across the internal resistance from the EMF of the battery. Mathematically, it’s expressed as:
\[
V_{\text{term}} = \text{EMF} - I \cdot r_{\text{int}}
\]
This means that the terminal voltage will always be less than the EMF because of the internal voltage drop.
### Practical Example
Consider a battery with an EMF of 12 volts and an internal resistance of 1 ohm. If the battery is supplying a current of 2 amperes, the voltage drop due to internal resistance is:
\[
V_{\text{drop}} = I \cdot r_{\text{int}} = 2 \text{ A} \cdot 1 \text{ }\Omega = 2 \text{ V}
\]
Thus, the terminal voltage is:
\[
V_{\text{term}} = \text{EMF} - V_{\text{drop}} = 12 \text{ V} - 2 \text{ V} = 10 \text{ V}
\]
### Conclusion
In summary, the terminal voltage of a battery is typically less than its EMF due to the internal resistance causing a voltage drop when current flows. The EMF represents the ideal maximum voltage when no current is flowing, while the terminal voltage represents the practical voltage available under load.
### Key Concepts
1. **Electromotive Force (EMF):** EMF is the maximum potential difference between the terminals of a battery when no current is flowing. It represents the battery’s ability to drive current through a circuit.
2. **Terminal Voltage:** Terminal voltage is the actual voltage available across the terminals of the battery when current is flowing. It is the voltage you measure when the battery is connected to a load and current is flowing through the circuit.
### Why Terminal Voltage is Less than EMF
When a battery is providing current to a circuit, the terminal voltage is affected by the internal resistance of the battery. Here’s how it works:
1. **Internal Resistance:** Every real battery has some internal resistance (denoted as \( r_{\text{int}} \)). This resistance causes a voltage drop inside the battery when current flows.
2. **Ohm’s Law and Voltage Drop:** According to Ohm’s Law, the voltage drop across the internal resistance of the battery is given by \( V_{\text{drop}} = I \cdot r_{\text{int}} \), where \( I \) is the current flowing through the circuit. This voltage drop occurs within the battery itself.
3. **Terminal Voltage Calculation:** The terminal voltage (\( V_{\text{term}} \)) can be found by subtracting the voltage drop across the internal resistance from the EMF of the battery. Mathematically, it’s expressed as:
\[
V_{\text{term}} = \text{EMF} - I \cdot r_{\text{int}}
\]
This means that the terminal voltage will always be less than the EMF because of the internal voltage drop.
### Practical Example
Consider a battery with an EMF of 12 volts and an internal resistance of 1 ohm. If the battery is supplying a current of 2 amperes, the voltage drop due to internal resistance is:
\[
V_{\text{drop}} = I \cdot r_{\text{int}} = 2 \text{ A} \cdot 1 \text{ }\Omega = 2 \text{ V}
\]
Thus, the terminal voltage is:
\[
V_{\text{term}} = \text{EMF} - V_{\text{drop}} = 12 \text{ V} - 2 \text{ V} = 10 \text{ V}
\]
### Conclusion
In summary, the terminal voltage of a battery is typically less than its EMF due to the internal resistance causing a voltage drop when current flows. The EMF represents the ideal maximum voltage when no current is flowing, while the terminal voltage represents the practical voltage available under load.
Terminal voltage can be more than the electromotive force (EMF) in certain scenarios, particularly when charging a battery. Here's why:
1. **Charging a Battery**: When a battery is being charged, an external power supply applies a voltage greater than the battery's EMF to push current into the battery. In this case, the terminal voltage (which is the voltage across the battery's terminals) exceeds the EMF. This is because the external supply is overcoming the internal resistance of the battery and causing the battery to gain charge.
2. **Counter EMF (Back EMF)**: In devices like motors, the terminal voltage can exceed the back EMF (the voltage generated in opposition to the supply voltage) when running the motor at high loads or speeds. The terminal voltage is often controlled to be higher than the back EMF to keep the motor running efficiently.
In most cases, however, the terminal voltage is lower than the EMF due to internal resistance, but charging or special operating conditions can make the terminal voltage higher than the EMF.
1. **Charging a Battery**: When a battery is being charged, an external power supply applies a voltage greater than the battery's EMF to push current into the battery. In this case, the terminal voltage (which is the voltage across the battery's terminals) exceeds the EMF. This is because the external supply is overcoming the internal resistance of the battery and causing the battery to gain charge.
2. **Counter EMF (Back EMF)**: In devices like motors, the terminal voltage can exceed the back EMF (the voltage generated in opposition to the supply voltage) when running the motor at high loads or speeds. The terminal voltage is often controlled to be higher than the back EMF to keep the motor running efficiently.
In most cases, however, the terminal voltage is lower than the EMF due to internal resistance, but charging or special operating conditions can make the terminal voltage higher than the EMF.