A cable of resistance `10 Omega` carries electric power from a generator producing `250 kW at 10,000 V`. The current in the cable is

Options

A. `1000 A`
B. `250 A`
C. `100 A`
D. `25 A`

Explanation

To find the current in the cable, we can use the relationship between power, voltage, and current, which is given by the formula:

\[ P = V \times I \]

Where:
- \( P \) is the power (in watts),
- \( V \) is the voltage (in volts),
- \( I \) is the current (in amperes).

### Step-by-Step Solution:

1. **Convert Power from Kilowatts to Watts**:
Given power \( P = 250 \, \text{kW} \).
\[ P = 250 \times 10^3 \, \text{W} = 250000 \, \text{W} \]

2. **Identify the Voltage**:
The voltage \( V \) is given as:
\[ V = 10000 \, \text{V} \]

3. **Rearrange the Power Formula to Solve for Current**:
We can rearrange the formula \( P = V \times I \) to find the current \( I \):
\[ I = \frac{P}{V} \]

4. **Substitute the Known Values**:
Now, substitute the values of \( P \) and \( V \) into the equation:
\[ I = \frac{250000 \, \text{W}}{10000 \, \text{V}} \]

5. **Calculate the Current**:
Performing the division:
\[ I = \frac{250000}{10000} = 25 \, \text{A} \]

### Final Answer:
The current in the cable is \( 25 \, \text{A} \).

---