Why is the terminal voltage less than the electromotive force of the battery?
2 Answers
The terminal voltage of a battery is often less than its electromotive force (EMF) due to the internal resistance of the battery. To understand why this happens, let's break down the concepts involved:
### Electromotive Force (EMF)
- **Definition**: The EMF of a battery is a measure of the energy provided per charge by the battery's chemical reactions. It represents the maximum potential difference between the two terminals of the battery when no current is flowing (open-circuit condition).
### Internal Resistance
- **Definition**: Every real battery has some internal resistance, which is the opposition to the flow of current within the battery itself. This resistance is due to the materials and chemical processes inside the battery.
### How Internal Resistance Affects Terminal Voltage
1. **Current Flow and Voltage Drop**: When a battery is supplying current to an external circuit, the internal resistance causes a voltage drop within the battery. This drop is given by Ohm's law:
\[ V_{\text{drop}} = I \cdot R_{\text{internal}} \]
where \( I \) is the current flowing through the battery, and \( R_{\text{internal}} \) is the internal resistance of the battery.
2. **Terminal Voltage**: The terminal voltage (\( V_{\text{terminal}} \)) is the voltage measured across the battery's terminals when it is connected to a circuit and current is flowing. This voltage is less than the EMF due to the internal voltage drop caused by the internal resistance. The relationship can be expressed as:
\[ V_{\text{terminal}} = \text{EMF} - V_{\text{drop}} \]
Substituting the voltage drop:
\[ V_{\text{terminal}} = \text{EMF} - (I \cdot R_{\text{internal}}) \]
### Example
Imagine a battery with an EMF of 12 volts and an internal resistance of 1 ohm. If the battery is supplying a current of 2 amps, the voltage drop inside the battery is:
\[ V_{\text{drop}} = I \cdot R_{\text{internal}} = 2 \, \text{A} \cdot 1 \, \text{Ω} = 2 \, \text{V} \]
Thus, the terminal voltage when the battery is under load is:
\[ V_{\text{terminal}} = \text{EMF} - V_{\text{drop}} = 12 \, \text{V} - 2 \, \text{V} = 10 \, \text{V} \]
### Summary
The terminal voltage of a battery is less than its EMF because of the internal resistance that causes a voltage drop when current flows. The internal resistance causes a reduction in the potential difference between the terminals under load, which is why you observe a lower voltage across the terminals compared to the EMF when the battery is not connected to a circuit.
### Electromotive Force (EMF)
- **Definition**: The EMF of a battery is a measure of the energy provided per charge by the battery's chemical reactions. It represents the maximum potential difference between the two terminals of the battery when no current is flowing (open-circuit condition).
### Internal Resistance
- **Definition**: Every real battery has some internal resistance, which is the opposition to the flow of current within the battery itself. This resistance is due to the materials and chemical processes inside the battery.
### How Internal Resistance Affects Terminal Voltage
1. **Current Flow and Voltage Drop**: When a battery is supplying current to an external circuit, the internal resistance causes a voltage drop within the battery. This drop is given by Ohm's law:
\[ V_{\text{drop}} = I \cdot R_{\text{internal}} \]
where \( I \) is the current flowing through the battery, and \( R_{\text{internal}} \) is the internal resistance of the battery.
2. **Terminal Voltage**: The terminal voltage (\( V_{\text{terminal}} \)) is the voltage measured across the battery's terminals when it is connected to a circuit and current is flowing. This voltage is less than the EMF due to the internal voltage drop caused by the internal resistance. The relationship can be expressed as:
\[ V_{\text{terminal}} = \text{EMF} - V_{\text{drop}} \]
Substituting the voltage drop:
\[ V_{\text{terminal}} = \text{EMF} - (I \cdot R_{\text{internal}}) \]
### Example
Imagine a battery with an EMF of 12 volts and an internal resistance of 1 ohm. If the battery is supplying a current of 2 amps, the voltage drop inside the battery is:
\[ V_{\text{drop}} = I \cdot R_{\text{internal}} = 2 \, \text{A} \cdot 1 \, \text{Ω} = 2 \, \text{V} \]
Thus, the terminal voltage when the battery is under load is:
\[ V_{\text{terminal}} = \text{EMF} - V_{\text{drop}} = 12 \, \text{V} - 2 \, \text{V} = 10 \, \text{V} \]
### Summary
The terminal voltage of a battery is less than its EMF because of the internal resistance that causes a voltage drop when current flows. The internal resistance causes a reduction in the potential difference between the terminals under load, which is why you observe a lower voltage across the terminals compared to the EMF when the battery is not connected to a circuit.
The terminal voltage of a battery is often less than its electromotive force (EMF) due to **internal resistance**. Here's why:
1. **Electromotive Force (EMF)**: This is the ideal voltage a battery provides when no current is flowing, representing the energy supplied per unit charge. It's essentially the maximum potential difference the battery can provide.
2. **Internal Resistance**: Every real battery has some internal resistance due to the materials and construction of the battery. When a current flows, a voltage drop occurs across this internal resistance. This voltage drop is given by \( V_{drop} = I \times r \), where:
- \( I \) is the current,
- \( r \) is the internal resistance of the battery.
3. **Terminal Voltage**: The voltage measured across the terminals of the battery while it's delivering current is called the terminal voltage. It's given by:
\[
V_{terminal} = EMF - I \times r
\]
As current flows, the voltage drop across the internal resistance reduces the terminal voltage compared to the EMF.
In summary, the terminal voltage is less than the EMF when the battery is supplying current because part of the EMF is used to overcome the internal resistance of the battery.
1. **Electromotive Force (EMF)**: This is the ideal voltage a battery provides when no current is flowing, representing the energy supplied per unit charge. It's essentially the maximum potential difference the battery can provide.
2. **Internal Resistance**: Every real battery has some internal resistance due to the materials and construction of the battery. When a current flows, a voltage drop occurs across this internal resistance. This voltage drop is given by \( V_{drop} = I \times r \), where:
- \( I \) is the current,
- \( r \) is the internal resistance of the battery.
3. **Terminal Voltage**: The voltage measured across the terminals of the battery while it's delivering current is called the terminal voltage. It's given by:
\[
V_{terminal} = EMF - I \times r
\]
As current flows, the voltage drop across the internal resistance reduces the terminal voltage compared to the EMF.
In summary, the terminal voltage is less than the EMF when the battery is supplying current because part of the EMF is used to overcome the internal resistance of the battery.