Why potential difference is always less than emf in a closed circuit?
2 Answers
The relationship between potential difference (voltage across components) and electromotive force (EMF) can be explained through several key concepts in electrical circuits:
1. **Definition**:
- **EMF**: The electromotive force (EMF) of a source (like a battery) is the maximum potential difference it can provide when no current is flowing (open circuit condition).
- **Potential Difference**: The potential difference across a component in a circuit (like a resistor) is the voltage drop that occurs when current flows through that component.
2. **Internal Resistance**:
- Every real power source (battery, generator) has some internal resistance. When current flows, there is a voltage drop across this internal resistance, which reduces the voltage available to external components in the circuit. This can be expressed as:
\[
V = \text{EMF} - I \cdot r_{\text{internal}}
\]
where \(I\) is the current and \(r_{\text{internal}}\) is the internal resistance. As a result, the potential difference across the load is always less than the EMF.
3. **Energy Considerations**:
- When current flows through the circuit, energy is dissipated in the form of heat in the resistive elements (including the internal resistance of the power source). This energy loss means that not all of the EMF is converted into useful work; thus, the potential difference measured across the load is lower than the EMF.
4. **Practical Implications**:
- In practical circuits, if the internal resistance is significant, the difference between the EMF and the potential difference can be quite noticeable, especially under high load conditions.
In summary, the potential difference across components in a closed circuit is always less than the EMF due to internal resistance and energy losses associated with current flow.
1. **Definition**:
- **EMF**: The electromotive force (EMF) of a source (like a battery) is the maximum potential difference it can provide when no current is flowing (open circuit condition).
- **Potential Difference**: The potential difference across a component in a circuit (like a resistor) is the voltage drop that occurs when current flows through that component.
2. **Internal Resistance**:
- Every real power source (battery, generator) has some internal resistance. When current flows, there is a voltage drop across this internal resistance, which reduces the voltage available to external components in the circuit. This can be expressed as:
\[
V = \text{EMF} - I \cdot r_{\text{internal}}
\]
where \(I\) is the current and \(r_{\text{internal}}\) is the internal resistance. As a result, the potential difference across the load is always less than the EMF.
3. **Energy Considerations**:
- When current flows through the circuit, energy is dissipated in the form of heat in the resistive elements (including the internal resistance of the power source). This energy loss means that not all of the EMF is converted into useful work; thus, the potential difference measured across the load is lower than the EMF.
4. **Practical Implications**:
- In practical circuits, if the internal resistance is significant, the difference between the EMF and the potential difference can be quite noticeable, especially under high load conditions.
In summary, the potential difference across components in a closed circuit is always less than the EMF due to internal resistance and energy losses associated with current flow.
In a closed electrical circuit, the **potential difference (V)** across the terminals of a power source (like a battery) is always less than the **electromotive force (emf, ε)** due to energy losses within the source itself, primarily caused by **internal resistance (r)**. Here's a detailed explanation of why this happens:
### 1. **What is Electromotive Force (emf)?**
The electromotive force (emf) is the total energy per unit charge that a power source, such as a battery or generator, can provide. It is the ideal potential difference across the terminals of the source when no current is flowing, meaning in an **open circuit**.
Mathematically, it’s defined as the work done to move a charge around the entire circuit, including both the external and internal parts of the circuit. Therefore, emf is the maximum potential difference that can be obtained from a source.
### 2. **What is Potential Difference (V)?**
The potential difference (or voltage) across the terminals of a power source in a **closed circuit** (when current is flowing) is the actual voltage available to drive current through the external circuit (resistors, devices, etc.). This is the usable voltage that we can measure across the external components connected to the circuit.
### 3. **Internal Resistance (r)**
Every real battery or power source has some internal resistance due to the materials it’s made of and the chemical processes that generate electrical energy. This **internal resistance (r)** is the opposition to current flow inside the battery itself, which causes energy to be lost as heat when the current flows.
This is why we cannot get the full emf when the circuit is closed and current flows. The energy that could have been provided to the external circuit is partially lost within the battery due to this internal resistance.
### 4. **Energy Loss in a Closed Circuit**
When the circuit is closed, the current (I) flows through both the internal resistance (r) and the external load (resistor, light bulb, etc.). According to Ohm's Law, the voltage drop across the internal resistance is:
\[
\text{Voltage drop across internal resistance} = I \times r
\]
This voltage drop is subtracted from the emf to give the actual potential difference across the terminals of the battery, which is less than the emf.
### 5. **Equation of the Closed Circuit**
The relationship between emf, internal resistance, and potential difference in a closed circuit can be described by the equation:
\[
\text{emf} = V + I \times r
\]
Where:
- **emf** is the electromotive force,
- **V** is the potential difference across the external circuit (what’s available for the external components),
- **I** is the current in the circuit,
- **r** is the internal resistance of the power source.
Rearranging the formula, we get:
\[
V = \text{emf} - I \times r
\]
This equation shows that the actual potential difference (V) is always less than the emf by an amount equal to the voltage drop due to the internal resistance \( (I \times r) \).
### 6. **Conclusion: Why is Potential Difference Less Than emf?**
In a closed circuit, some of the energy provided by the source (the emf) is "used up" in overcoming the internal resistance of the source itself. This results in a voltage drop inside the source, and thus the potential difference across the terminals of the source (what is available for the external circuit) is always less than the total emf.
If there were no internal resistance (which is an ideal but not realistic case), the potential difference would be equal to the emf. However, in practical, real-world situations, internal resistance always causes the potential difference to be less than the emf. The larger the internal resistance or the current, the greater the difference between the emf and the potential difference.
### 1. **What is Electromotive Force (emf)?**
The electromotive force (emf) is the total energy per unit charge that a power source, such as a battery or generator, can provide. It is the ideal potential difference across the terminals of the source when no current is flowing, meaning in an **open circuit**.
Mathematically, it’s defined as the work done to move a charge around the entire circuit, including both the external and internal parts of the circuit. Therefore, emf is the maximum potential difference that can be obtained from a source.
### 2. **What is Potential Difference (V)?**
The potential difference (or voltage) across the terminals of a power source in a **closed circuit** (when current is flowing) is the actual voltage available to drive current through the external circuit (resistors, devices, etc.). This is the usable voltage that we can measure across the external components connected to the circuit.
### 3. **Internal Resistance (r)**
Every real battery or power source has some internal resistance due to the materials it’s made of and the chemical processes that generate electrical energy. This **internal resistance (r)** is the opposition to current flow inside the battery itself, which causes energy to be lost as heat when the current flows.
This is why we cannot get the full emf when the circuit is closed and current flows. The energy that could have been provided to the external circuit is partially lost within the battery due to this internal resistance.
### 4. **Energy Loss in a Closed Circuit**
When the circuit is closed, the current (I) flows through both the internal resistance (r) and the external load (resistor, light bulb, etc.). According to Ohm's Law, the voltage drop across the internal resistance is:
\[
\text{Voltage drop across internal resistance} = I \times r
\]
This voltage drop is subtracted from the emf to give the actual potential difference across the terminals of the battery, which is less than the emf.
### 5. **Equation of the Closed Circuit**
The relationship between emf, internal resistance, and potential difference in a closed circuit can be described by the equation:
\[
\text{emf} = V + I \times r
\]
Where:
- **emf** is the electromotive force,
- **V** is the potential difference across the external circuit (what’s available for the external components),
- **I** is the current in the circuit,
- **r** is the internal resistance of the power source.
Rearranging the formula, we get:
\[
V = \text{emf} - I \times r
\]
This equation shows that the actual potential difference (V) is always less than the emf by an amount equal to the voltage drop due to the internal resistance \( (I \times r) \).
### 6. **Conclusion: Why is Potential Difference Less Than emf?**
In a closed circuit, some of the energy provided by the source (the emf) is "used up" in overcoming the internal resistance of the source itself. This results in a voltage drop inside the source, and thus the potential difference across the terminals of the source (what is available for the external circuit) is always less than the total emf.
If there were no internal resistance (which is an ideal but not realistic case), the potential difference would be equal to the emf. However, in practical, real-world situations, internal resistance always causes the potential difference to be less than the emf. The larger the internal resistance or the current, the greater the difference between the emf and the potential difference.