Question

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

• A. 19.2 W
• B. 19.2 kW
• C. 19.2 J
• D. 12.2 kW

Answer 1

The Correct Option is B

To determine the power loss in the copper wire, we need to consider the total voltage drop across the wire, the total resistance of the wire, and apply the formula for power loss.

1. Calculate the Total Voltage Drop:
   The total voltage drop (\( V \)) over the entire distance can be calculated by multiplying the fall of potential per km by the total distance in km:
   V = \text{Voltage drop per km} \times \text{Distance in km} = 8 \, \text{V/km} \times 150 \, \text{km} = 1200 \, \text{V}
2. Calculate the Total Resistance:
   The total resistance (\( R \)) of the wire is given by the product of resistance per km and the total distance in km:
   R = \text{Resistance per km} \times \text{Distance in km} = 0.5 \, \Omega/\text{km} \times 150 \, \text{km} = 75 \, \Omega
3. Calculate the Current:
   Using Ohm’s law, the current (\( I \)) flowing through the wire can be found by:
   I = \frac{V}{R} = \frac{1200 \, \text{V}}{75 \, \Omega} = 16 \, \text{A}
4. Calculate the Power Loss:
   The power loss (\( P \)) in the wire is calculated using the formula:
   P = I^2 \times R = (16 \, \text{A})^2 \times 75 \, \Omega = 256 \times 75 = 19200 \, \text{W} = 19.2 \, \text{kW}

Therefore, the power loss in the wire is 19.2 kW.