A battery of emf `2.0 V` and internal resistance `0.10 Omega` is being charged with a current of `5.0 A`. Find the potential difference between the terminals of the battery?

Explanation

To find the potential difference between the terminals of a battery that is being charged, we can use the formula:

\[ V = E + I \cdot R \]

Where:
- \( V \) is the potential difference between the terminals of the battery.
- \( E \) is the electromotive force (emf) of the battery.
- \( I \) is the charging current.
- \( R \) is the internal resistance of the battery.

### Step-by-step Solution:

1. **Identify the given values:**
- Emf of the battery, \( E = 2.0 \, \text{V} \)
- Internal resistance, \( R = 0.10 \, \Omega \)
- Charging current, \( I = 5.0 \, \text{A} \)

2. **Substitute the values into the formula:**
\[ V = E + I \cdot R \]
\[ V = 2.0 \, \text{V} + (5.0 \, \text{A} \cdot 0.10 \, \Omega) \]

3. **Calculate the product \( I \cdot R \):**
\[ I \cdot R = 5.0 \, \text{A} \cdot 0.10 \, \Omega = 0.50 \, \text{V} \]

4. **Add the values to find \( V \):**
\[ V = 2.0 \, \text{V} + 0.50 \, \text{V} = 2.50 \, \text{V} \]

5. **Conclusion:**
The potential difference between the terminals of the battery is \( 2.50 \, \text{V} \).