When current supplied by a cell to a circuit is `0.3 A`, its terminal potential difference is 0.9 A. When the current supplied becomes 0.2 A, its terminal potential difference becomes 1.0 V . The internal resistance of the cell is

Options

A. `0.5 Omega`
B. `2Omega`
C. ` 1.2 Omega`
D. `1 Omega `

Answer

To find the internal resistance of the cell, we can use the information provided about the terminal potential difference and the current supplied in two different scenarios.

### Step-by-Step Solution:

1. **Understand the relationship**: The terminal potential difference (V) of a cell is given by the formula:
\[ V = \epsilon - I \cdot R \]
where:
- \( V \) is the terminal potential difference,
- \( \epsilon \) is the electromotive force (emf) of the cell,
- \( I \) is the current flowing through the cell,
- \( R \) is the internal resistance of the cell.

2. **Set up equations for both scenarios**:
- For the first scenario where \( I = 0.3 \, A \) and \( V = 0.9 \, V \):
\[ 0.9 = \epsilon - 0.3R \quad \text{(Equation 1)} \]
- For the second scenario where \( I = 0.2 \, A \) and \( V = 1.0 \, V \):
\[ 1.0 = \epsilon - 0.2R \quad \text{(Equation 2)} \]

3. **Subtract Equation 1 from Equation 2**:
\[ (1.0 - 0.9) = (\epsilon - 0.2R) - (\epsilon - 0.3R) \]
Simplifying this gives:
\[ 0.1 = 0.3R - 0.2R \]
\[ 0.1 = 0.1R \]

4. **Solve for \( R \)**:
\[ R = \frac{0.1}{0.1} = 1 \, \Omega \]

5. **Conclusion**: The internal resistance of the cell is \( 1 \, \Omega \).