Why is the potential difference always less than emf in a closed circuit?
2 Answers
The potential difference across the terminals of a power source (like a battery) in a closed circuit is often less than the electromotive force (EMF) of that power source. Here’s a detailed explanation of why this happens:
### Understanding EMF and Potential Difference
1. **EMF (Electromotive Force):** This is the maximum potential difference that a power source can provide when no current is flowing through the circuit. It's essentially the work done per unit charge by the source to move charges through the circuit. It represents the ideal or theoretical maximum voltage the power source can deliver.
2. **Potential Difference:** This is the actual voltage measured across the terminals of the power source when a current is flowing through the circuit. It’s what you measure when the circuit is complete and current is flowing.
### Why the Potential Difference is Less Than EMF
1. **Internal Resistance:** All real power sources have some internal resistance, which is the resistance of the power source itself (like the internal components of a battery). This resistance is crucial because it affects how the power source behaves in a real circuit.
2. **Voltage Drop Across Internal Resistance:** When current flows through the circuit, some of the energy provided by the power source is used to overcome its own internal resistance. This results in a voltage drop inside the power source. The internal resistance causes a drop in the potential difference between the terminals.
3. **Ohm’s Law and Internal Resistance:** The relationship between EMF (E), terminal potential difference (V), internal resistance (r), and current (I) can be described by the formula:
\[
E = V + I \cdot r
\]
Rearranging this formula gives us:
\[
V = E - I \cdot r
\]
This shows that the terminal potential difference \( V \) is equal to the EMF \( E \) minus the voltage drop \( I \cdot r \) across the internal resistance of the power source.
4. **Practical Example:** Consider a battery with an EMF of 12V and an internal resistance of 1 ohm. If the battery is supplying a current of 2A, the voltage drop across the internal resistance is:
\[
I \cdot r = 2 \, \text{A} \times 1 \, \text{ohm} = 2 \, \text{V}
\]
The potential difference across the battery terminals, when the current is flowing, would be:
\[
V = E - I \cdot r = 12 \, \text{V} - 2 \, \text{V} = 10 \, \text{V}
\]
So, the potential difference is less than the EMF by the amount of voltage drop caused by the internal resistance.
### Summary
In summary, the potential difference across the terminals of a power source is always less than its EMF in a closed circuit due to the voltage drop across the internal resistance of the power source. This internal resistance consumes some of the electrical energy that would otherwise contribute to the potential difference across the terminals.
### Understanding EMF and Potential Difference
1. **EMF (Electromotive Force):** This is the maximum potential difference that a power source can provide when no current is flowing through the circuit. It's essentially the work done per unit charge by the source to move charges through the circuit. It represents the ideal or theoretical maximum voltage the power source can deliver.
2. **Potential Difference:** This is the actual voltage measured across the terminals of the power source when a current is flowing through the circuit. It’s what you measure when the circuit is complete and current is flowing.
### Why the Potential Difference is Less Than EMF
1. **Internal Resistance:** All real power sources have some internal resistance, which is the resistance of the power source itself (like the internal components of a battery). This resistance is crucial because it affects how the power source behaves in a real circuit.
2. **Voltage Drop Across Internal Resistance:** When current flows through the circuit, some of the energy provided by the power source is used to overcome its own internal resistance. This results in a voltage drop inside the power source. The internal resistance causes a drop in the potential difference between the terminals.
3. **Ohm’s Law and Internal Resistance:** The relationship between EMF (E), terminal potential difference (V), internal resistance (r), and current (I) can be described by the formula:
\[
E = V + I \cdot r
\]
Rearranging this formula gives us:
\[
V = E - I \cdot r
\]
This shows that the terminal potential difference \( V \) is equal to the EMF \( E \) minus the voltage drop \( I \cdot r \) across the internal resistance of the power source.
4. **Practical Example:** Consider a battery with an EMF of 12V and an internal resistance of 1 ohm. If the battery is supplying a current of 2A, the voltage drop across the internal resistance is:
\[
I \cdot r = 2 \, \text{A} \times 1 \, \text{ohm} = 2 \, \text{V}
\]
The potential difference across the battery terminals, when the current is flowing, would be:
\[
V = E - I \cdot r = 12 \, \text{V} - 2 \, \text{V} = 10 \, \text{V}
\]
So, the potential difference is less than the EMF by the amount of voltage drop caused by the internal resistance.
### Summary
In summary, the potential difference across the terminals of a power source is always less than its EMF in a closed circuit due to the voltage drop across the internal resistance of the power source. This internal resistance consumes some of the electrical energy that would otherwise contribute to the potential difference across the terminals.
In a closed circuit, the potential difference across the terminals of a power source (like a battery) is always less than its electromotive force (EMF) due to the internal resistance of the power source.
Here's a breakdown of why this happens:
1. **Internal Resistance**: Every real power source, such as a battery, has some internal resistance \( r \). This internal resistance causes a voltage drop within the power source itself when current flows through it.
2. **Ohm's Law for Internal Resistance**: The voltage drop across the internal resistance can be calculated using Ohm's Law: \( V_{drop} = I \cdot r \), where \( I \) is the current flowing through the circuit, and \( r \) is the internal resistance.
3. **Potential Difference Across Terminals**: The potential difference \( V \) across the terminals of the battery is the EMF \( \mathcal{E} \) minus the voltage drop due to the internal resistance. Mathematically, it can be expressed as:
\[
V = \mathcal{E} - I \cdot r
\]
4. **Effect of Current**: When there is no current flowing (open circuit), the potential difference across the terminals equals the EMF. However, when the circuit is closed and current flows, the internal resistance causes a voltage drop, making the potential difference across the terminals less than the EMF.
So, in summary, the internal resistance of the power source causes the potential difference across its terminals to be less than the EMF when there is current flowing in the circuit.
Here's a breakdown of why this happens:
1. **Internal Resistance**: Every real power source, such as a battery, has some internal resistance \( r \). This internal resistance causes a voltage drop within the power source itself when current flows through it.
2. **Ohm's Law for Internal Resistance**: The voltage drop across the internal resistance can be calculated using Ohm's Law: \( V_{drop} = I \cdot r \), where \( I \) is the current flowing through the circuit, and \( r \) is the internal resistance.
3. **Potential Difference Across Terminals**: The potential difference \( V \) across the terminals of the battery is the EMF \( \mathcal{E} \) minus the voltage drop due to the internal resistance. Mathematically, it can be expressed as:
\[
V = \mathcal{E} - I \cdot r
\]
4. **Effect of Current**: When there is no current flowing (open circuit), the potential difference across the terminals equals the EMF. However, when the circuit is closed and current flows, the internal resistance causes a voltage drop, making the potential difference across the terminals less than the EMF.
So, in summary, the internal resistance of the power source causes the potential difference across its terminals to be less than the EMF when there is current flowing in the circuit.