Two cities are 150 km apart. Electric power is sent from one city to antoerh city through copper wires. The fal of potential per km is 8 volt and the average resistance per km is `0.5Omega`. The power loss in the wire is

Options

A. 19.2 W
B. 19.2 W
C. 12.2 W
D. 12.2 W

Explanation

To solve the problem of power loss in the wire, we can follow these steps:

### Step 1: Calculate the Total Potential Drop
The potential drop per kilometer is given as 8 volts. Since the distance between the two cities is 150 km, we can calculate the total potential drop (V_total) as follows:

\[ V_{\text{total}} = \text{Potential drop per km} \times \text{Distance in km} \]
\[ V_{\text{total}} = 8 \, \text{V/km} \times 150 \, \text{km} = 1200 \, \text{V} \]

### Step 2: Calculate the Total Resistance
The average resistance per kilometer is given as 0.5 ohms. Therefore, the total resistance (R_total) over the distance of 150 km can be calculated as:

\[ R_{\text{total}} = \text{Resistance per km} \times \text{Distance in km} \]
\[ R_{\text{total}} = 0.5 \, \Omega/\text{km} \times 150 \, \text{km} = 75 \, \Omega \]

### Step 3: Calculate the Power Loss
The power loss (P) in the wire can be calculated using the formula:

\[ P = \frac{V_{\text{total}}^2}{R_{\text{total}}} \]
Substituting the values we found:

\[ P = \frac{(1200 \, \text{V})^2}{75 \, \Omega} \]
\[ P = \frac{1440000 \, \text{V}^2}{75 \, \Omega} = 19200 \, \text{W} \]

### Step 4: Convert Power Loss to Kilowatts
To express the power loss in kilowatts (kW), we divide by 1000:

\[ P = \frac{19200 \, \text{W}}{1000} = 19.2 \, \text{kW} \]

### Final Answer
The power loss in the wire is **19.2 kW**.

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