A cell of 2.1 V gives 0.2 A current through resistance `10Omega` The internal resistance is:

Options

A. `5 Omega`
B. `50 Omega`
C. `0.05Omega`
D. `0.5 Omega`

Explanation

To find the internal resistance of the cell, we can use the formula relating the electromotive force (emf), current, external resistance, and internal resistance. The formula is given by:

\[ E = I(R + r) \]

Where:
- \( E \) is the emf of the cell (2.1 V),
- \( I \) is the current (0.2 A),
- \( R \) is the external resistance (10 Ω),
- \( r \) is the internal resistance (which we want to find).

### Step-by-Step Solution:

1. **Identify the known values:**
- \( E = 2.1 \, \text{V} \)
- \( I = 0.2 \, \text{A} \)
- \( R = 10 \, \Omega \)

2. **Substitute the known values into the formula:**
\[ 2.1 = 0.2 \times (10 + r) \]

3. **Distribute the current \( I \) across the sum of resistances:**
\[ 2.1 = 0.2 \times 10 + 0.2r \]
\[ 2.1 = 2 + 0.2r \]

4. **Isolate the term with \( r \):**
\[ 2.1 - 2 = 0.2r \]
\[ 0.1 = 0.2r \]

5. **Solve for \( r \):**
\[ r = \frac{0.1}{0.2} = 0.5 \, \Omega \]

### Conclusion:
The internal resistance of the cell is \( 0.5 \, \Omega \).

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