A battery is charged at a potential fo 15 V for 8 h when the current folwing is 10A. The battery on discharge supplies a current of 5A fo 15h . The mean terminal voltage during discharge is 14V. The watt-hour efficiency of the battery is

Options

A. 0.825
B. 0.8
C. 0.9
D. 0.875

Answer

To find the watt-hour efficiency of the battery, we need to calculate both the energy input during charging and the energy output during discharging, and then use these values to find the efficiency.

### Step-by-Step Solution:

1. **Calculate the Energy Input (Charging Energy)**:
- The formula for energy is given by:
\[ E = V \times I \times T \]
- Where:
- \( V = 15 \, \text{V} \) (voltage during charging)
- \( I = 10 \, \text{A} \) (current during charging)
- \( T = 8 \, \text{h} \) (time of charging)
- Substituting the values:
\[ E_{\text{input}} = 15 \, \text{V} \times 10 \, \text{A} \times 8 \, \text{h} = 1200 \, \text{Wh} \]

2. **Calculate the Energy Output (Discharging Energy)**:
- The formula for energy is the same:
\[ E = V \times I \times T \]
- Where:
- \( V = 14 \, \text{V} \) (mean terminal voltage during discharge)
- \( I = 5 \, \text{A} \) (current during discharge)
- \( T = 15 \, \text{h} \) (time of discharging)
- Substituting the values:
\[ E_{\text{output}} = 14 \, \text{V} \times 5 \, \text{A} \times 15 \, \text{h} = 1050 \, \text{Wh} \]

3. **Calculate the Watt-Hour Efficiency**:
- The efficiency (\( \eta \)) can be calculated using the formula:
\[ \eta = \frac{E_{\text{output}}}{E_{\text{input}}} \]
- Substituting the values:
\[ \eta = \frac{1050 \, \text{Wh}}{1200 \, \text{Wh}} = 0.875 \]

4. **Convert Efficiency to Percentage**:
- To express the efficiency as a percentage, multiply by 100:
\[ \eta = 0.875 \times 100 = 87.5\% \]

### Final Answer:
The watt-hour efficiency of the battery is **87.5%**.