a cable of resistance 10 ohm carries electric power from a generator producing 250kw at 10000v , the power lost in the cable during transmission is

Options

A. `3.15 kW`
B. `12.5 kW`
C. `6.25 kW`
D. `25 kW`

Explanation

To solve the problem of finding the power lost in a cable during transmission, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Given Values**:
- Resistance of the cable, \( R = 10 \, \Omega \)
- Power generated by the generator, \( P = 250 \, \text{kW} = 250 \times 10^3 \, \text{W} \)
- Voltage supplied, \( V = 10,000 \, \text{V} \)

2. **Calculate the Current**:
The power can be expressed in terms of voltage and current using the formula:
\[ P = V \times I \]
Rearranging this gives:
\[ I = \frac{P}{V} \]
Substituting the known values:
\[ I = \frac{250 \times 10^3}{10,000} \]
Simplifying this:
\[ I = \frac{250,000}{10,000} = 25 \, \text{A} \]

3. **Calculate the Power Loss in the Cable**:
The power loss due to resistance in the cable can be calculated using the formula:
\[ P_{\text{loss}} = I^2 \times R \]
Substituting the values of current and resistance:
\[ P_{\text{loss}} = (25)^2 \times 10 \]
Calculating \( 25^2 \):
\[ 25^2 = 625 \]
Now, substituting this back:
\[ P_{\text{loss}} = 625 \times 10 = 6250 \, \text{W} \]

4. **Convert Power Loss to Kilowatts**:
To express the power loss in kilowatts:
\[ P_{\text{loss}} = \frac{6250}{1000} = 6.25 \, \text{kW} \]

5. **Final Result**:
The power lost in the cable during transmission is:
\[ \boxed{6.25 \, \text{kW}} \]