The emf of a battery is 2V and its internal resistance is `0.5Omega` the maximum power which it can deliver to any external circuit will be

Options

A. 8watt
B. 4watt
C. 2watt
D. none of the above

Explanation

To find the maximum power that can be delivered by a battery to an external circuit, we can use the formula derived from the maximum power transfer theorem. According to this theorem, the maximum power is delivered when the load resistance (R) is equal to the internal resistance (r) of the battery.

### Step-by-Step Solution:

1. **Identify the given values:**
- EMF of the battery (E) = 2 V
- Internal resistance of the battery (r) = 0.5 Ω

2. **Use the formula for maximum power (P_max):**
The maximum power delivered to the load can be calculated using the formula:
\[ P_{max} = \frac{E^2}{4r} \]

3. **Substitute the values into the formula:**
\[ P_{max} = \frac{(2)^2}{4 \times 0.5} \]

4. **Calculate the numerator:**
\[ (2)^2 = 4 \]

5. **Calculate the denominator:**
\[ 4 \times 0.5 = 2 \]

6. **Calculate the maximum power:**
\[ P_{max} = \frac{4}{2} = 2 \text{ W} \]

### Final Answer:
The maximum power which the battery can deliver to any external circuit is **2 Watts**.