Question

Why is the emf of a battery always slightly higher than the potential difference?

Answer 1

The electromotive force (emf) of a battery is always slightly higher than the potential difference across its terminals when it is connected to a circuit due to internal resistance. Let’s break this down in detail:

### 1. **Understanding emf and Potential Difference:**

- **Electromotive Force (emf):** The emf of a battery is the maximum potential difference that the battery can provide when no current is flowing. It’s essentially the battery’s ability to push electric charge through a circuit. Think of it as the voltage that the battery can provide in an ideal, no-load condition.

- **Potential Difference:** The potential difference across the battery terminals is the voltage measured when the battery is connected to a circuit and current is flowing. This voltage is less than the emf due to the internal resistance of the battery.

### 2. **Internal Resistance:**

- **Internal Resistance:** Inside every real battery, there is some resistance to the flow of electric current, known as internal resistance. This is due to the materials and construction of the battery, including the electrolyte and electrodes.

### 3. **Voltage Drop Due to Internal Resistance:**

When a battery is connected to a circuit, current flows through the battery’s internal resistance. According to Ohm's Law, the voltage drop across a resistor (in this case, the internal resistance \( r \)) is given by:

\[ V_{\text{drop}} = I \times r \]

where \( I \) is the current flowing through the circuit.

### 4. **Emf and Terminal Voltage Relationship:**

- **Terminal Voltage:** This is the voltage you measure across the battery’s terminals when it is in use, and it is less than the emf due to the internal resistance.

- The terminal voltage \( V_{\text{terminal}} \) is given by:

\[ V_{\text{terminal}} = \text{emf} - (I \times r) \]

Here, \( \text{emf} \) is the emf of the battery, \( I \) is the current, and \( r \) is the internal resistance.

### 5. **Why Emf is Higher:**

- When no current is flowing (open circuit condition), the potential difference across the terminals of the battery equals the emf because there is no voltage drop across the internal resistance.
  
- When current is flowing (closed circuit), the internal resistance causes a voltage drop within the battery, reducing the potential difference measured across the terminals compared to the emf.

Thus, under normal operating conditions with a current flowing, the emf of the battery is always slightly higher than the potential difference you measure across its terminals. The difference between these two values is the voltage drop due to the internal resistance of the battery.

Answer 2

The electromotive force (EMF) of a battery is always slightly higher than the potential difference (or terminal voltage) due to the internal resistance of the battery. Here's a detailed explanation of why this happens:

### Understanding EMF and Terminal Voltage

1. **Electromotive Force (EMF):**
   - **Definition:** EMF is the maximum potential difference that a battery can provide when no current is flowing through it. It represents the energy per unit charge that the battery can supply.
   - **Measurement:** EMF is typically measured under open-circuit conditions (when the battery is not connected to any external circuit).

2. **Terminal Voltage:**
   - **Definition:** Terminal voltage is the potential difference across the terminals of the battery when it is connected to an external circuit and current is flowing. This is the voltage that actually appears across the battery terminals.
   - **Measurement:** Terminal voltage is measured when the battery is supplying current to a load.

### Why EMF is Higher than Terminal Voltage

When a battery is connected to a circuit and current flows through it, there are two main factors to consider:

1. **Internal Resistance:**
   - **Concept:** Every battery has some internal resistance (denoted as \( r \)) due to the materials and construction of the battery.
   - **Impact:** When current \( I \) flows through the battery, a voltage drop occurs across this internal resistance according to Ohm's law (\( V = IR \)).

2. **Voltage Drop Across Internal Resistance:**
   - **Formula:** The voltage drop across the internal resistance of the battery is given by \( I \times r \), where \( I \) is the current flowing through the battery and \( r \) is the internal resistance.
   - **Effect on Terminal Voltage:** The terminal voltage \( V_{\text{terminal}} \) is given by the EMF minus the voltage drop across the internal resistance:
     \[
     V_{\text{terminal}} = \text{EMF} - I \times r
     \]
   - **Result:** As current flows through the battery, the terminal voltage is reduced by the amount of voltage lost due to the internal resistance. This is why the terminal voltage is always less than the EMF when the battery is supplying current.

### Summary

The EMF of a battery is always slightly higher than the potential difference (terminal voltage) because the internal resistance of the battery causes a voltage drop when current flows. The greater the current or the higher the internal resistance, the greater the voltage drop, and thus, the greater the difference between the EMF and the terminal voltage.