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Why the emf of a cell is always greater than its terminal voltage?

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The electromotive force (emf) of a cell is always greater than its terminal voltage due to the presence of internal resistance within the cell. Here's a detailed explanation of why this is the case:

### Definitions

1. **Emf (Electromotive Force):** The emf of a cell is the maximum potential difference between its terminals when no current is flowing through the cell. It represents the energy provided by the cell per unit charge.

2. **Terminal Voltage:** The terminal voltage is the potential difference between the terminals of the cell when current is flowing. This is the voltage you actually measure when the cell is connected to an external circuit.

### Internal Resistance and Its Effect

Cells have internal resistance, which is the resistance to the flow of current within the cell itself. This internal resistance affects the terminal voltage of the cell in the following way:

1. **Internal Resistance (r):** This is the resistance encountered by the current as it flows through the cell's internal components. It can be due to the electrolyte, electrodes, and other internal structures.

2. **Current (I):** When a current flows through the cell, it encounters the internal resistance.

### Relationship Between Emf, Terminal Voltage, and Internal Resistance

When a current \( I \) flows through a cell with internal resistance \( r \), the terminal voltage \( V_{\text{terminal}} \) can be described by the following equation:

\[ V_{\text{terminal}} = \text{emf} - I \cdot r \]

Here’s a breakdown of this equation:

- **Emf:** This is the voltage the cell would provide if no current were flowing.
- **\( I \cdot r \):** This term represents the voltage drop across the internal resistance due to the current.

### Explanation

- **Voltage Drop Across Internal Resistance:** When current flows through the internal resistance, a portion of the emf is used up in overcoming this resistance. This results in a reduction of the terminal voltage compared to the emf.

- **Terminal Voltage Less Than Emf:** Because the internal resistance causes a voltage drop as the current flows, the voltage available at the cell’s terminals (i.e., the terminal voltage) is less than the emf.

### Practical Example

Consider a simple example where a cell has an emf of 12V and an internal resistance of 1 ohm. If the cell supplies a current of 2A, the voltage drop across the internal resistance is:

\[ \text{Voltage Drop} = I \cdot r = 2 \, \text{A} \cdot 1 \, \text{ohm} = 2 \, \text{V} \]

Therefore, the terminal voltage is:

\[ V_{\text{terminal}} = \text{emf} - \text{Voltage Drop} = 12 \, \text{V} - 2 \, \text{V} = 10 \, \text{V} \]

In this case, the terminal voltage is 10V, which is less than the emf of 12V due to the internal resistance.

### Summary

The emf of a cell is always greater than its terminal voltage because of the internal resistance of the cell. The internal resistance causes a voltage drop when current flows, leading to a reduction in the terminal voltage compared to the emf.
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The electromotive force (EMF) of a cell is always greater than its terminal voltage due to internal resistance. Let's break down why this is the case:

### 1. **Electromotive Force (EMF)**

The EMF of a cell is the maximum potential difference between its terminals when no current is flowing. It represents the cell's ability to provide electrical energy. The EMF is determined by the cell's chemistry and is a characteristic of the cell itself.

### 2. **Terminal Voltage**

The terminal voltage of a cell is the potential difference measured across its terminals when a current is flowing through the circuit. This is the voltage you actually use when the cell is supplying power to a load.

### 3. **Internal Resistance**

Every real cell has some internal resistance, which is the resistance to the flow of current within the cell itself. When a current flows, a voltage drop occurs across this internal resistance due to Ohm's law (\( V = IR \)).

### 4. **Voltage Drop Due to Internal Resistance**

The relationship between EMF (\( E \)), terminal voltage (\( V \)), and internal resistance (\( r \)) can be described by the formula:
\[ V = E - Ir \]
where:
- \( E \) is the EMF of the cell.
- \( I \) is the current flowing through the cell.
- \( r \) is the internal resistance of the cell.

When current \( I \) flows through the cell, the internal resistance \( r \) causes a voltage drop \( Ir \). Thus, the terminal voltage \( V \) is reduced from the EMF by this amount.

### 5. **Why EMF is Always Greater**

Since \( V = E - Ir \), it’s clear that:
- As long as \( I \) and \( r \) are greater than zero, \( Ir \) will be a positive number.
- Therefore, \( E - Ir \) (terminal voltage) will always be less than \( E \) (EMF).

In other words, the internal resistance causes a loss of voltage inside the cell when a current is drawn. This is why the EMF of a cell is always greater than its terminal voltage during operation.

### 6. **Practical Example**

If you have a cell with an EMF of 10 volts and an internal resistance of 0.5 ohms, and you draw a current of 2 amps, the terminal voltage would be:
\[ V = E - Ir = 10V - (2A \times 0.5 \Omega) = 10V - 1V = 9V \]

Here, the terminal voltage (9V) is less than the EMF (10V) because of the voltage drop across the internal resistance.
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