Question

Why the potential difference of a source of electric current is always less than its emf?

Answer 1

The potential difference (or terminal voltage) of a source of electric current is always less than its electromotive force (emf) due to internal resistance. Here's a breakdown of why this happens:

1. **Emf Definition**: The emf of a source, such as a battery or generator, is the maximum potential difference it can provide when no current is flowing. It's essentially the work done per unit charge to move the charge through the source.

2. **Internal Resistance**: All real sources of electric current have some internal resistance, which is the resistance to current flow within the source itself. This resistance is due to the materials and construction of the source.

3. **Current Flow**: When a current flows through the source, a voltage drop occurs across the internal resistance. According to Ohm's law (\(V = IR\)), this drop (\(V_{drop}\)) is equal to the product of the current (\(I\)) and the internal resistance (\(r\)) of the source:  
   \[
   V_{drop} = I \times r
   \]

4. **Terminal Voltage**: The terminal voltage (\(V_t\)) is the actual voltage available at the terminals of the source when a current is drawn. It is given by the equation:
   \[
   V_t = \text{emf} - V_{drop} = \text{emf} - I \times r
   \]

Since \(I \times r\) is always a positive value when current is flowing, the terminal voltage will always be less than the emf:
   \[
   V_t < \text{emf}
   \]

5. **Implications**: This difference means that as more current is drawn from the source, the terminal voltage decreases further, which can affect the performance of electrical devices powered by the source.

In summary, the potential difference across a source is less than its emf because of the internal resistance that causes a voltage drop when current flows.

Answer 2

The potential difference (or voltage) across a source of electric current is always less than its electromotive force (emf) due to the internal resistance of the source. Here’s a detailed explanation:

### Understanding EMF and Potential Difference

1. **Electromotive Force (EMF):**
   - The EMF of a source, such as a battery or generator, is the maximum potential difference it can provide when no current is flowing. It represents the energy supplied per unit charge by the source.

2. **Potential Difference:**
   - The potential difference across the terminals of the source is the voltage that actually appears when current flows through the circuit. This is the voltage you measure between the terminals when the source is connected in a circuit.

### Internal Resistance and Its Effect

- **Internal Resistance (r):**
  - Every real source of emf has some internal resistance. This resistance is due to the materials and construction of the source itself. When current flows through the source, there is a voltage drop across this internal resistance.

### Voltage Drop and Relationship

1. **When No Current Flows:**
   - If no current flows (open circuit), the voltage across the terminals equals the EMF because there is no voltage drop due to internal resistance.

2. **When Current Flows:**
   - When current (I) flows through the circuit, a voltage drop occurs across the internal resistance of the source. This drop can be calculated using Ohm's Law: \( V_{drop} = I \cdot r \).
   - The potential difference (V) across the terminals is then given by the EMF minus the voltage drop:
     \[
     V = \text{EMF} - I \cdot r
     \]
   - As a result, the potential difference is always less than the EMF when there is a current flowing through the circuit.

### Example

Imagine a battery with an EMF of 12 volts and an internal resistance of 1 ohm. If the current flowing through the circuit is 2 amperes, the voltage drop across the internal resistance is:
\[
V_{drop} = 2 \text{ A} \times 1 \text{ Ω} = 2 \text{ V}
\]
The potential difference across the terminals of the battery would be:
\[
V = 12 \text{ V} - 2 \text{ V} = 10 \text{ V}
\]

### Summary

The potential difference across a source is always less than its EMF because the internal resistance of the source causes a voltage drop when current flows. The EMF represents the ideal maximum voltage the source can provide, while the actual potential difference in the circuit is reduced by the internal resistance.