Question

part a
for the transmission of electric power from power plant to homes, as depicted in the figure above, when the electric power sent by the plant is 100 kw at 12,000 v, what is the total resistance of the transmission line per unit length of ( 10^{-5}omega/m ) (the value taken into account all the wires of the transmission line)?
assume the total resistance of the transmission line per unit length of ( 10^{-5}omega/m ) (the value taken into account all the wires of the transmission line).
express your answer to one significant figure and include the appropriate units.

Explanation:

Step1: Calculate the current

Use the formula \(P = UI\), so \(I=\frac{P}{U}\). Given \(P = 100\times10^{3}\text{ W}\) and \(U = 12000\text{ V}\), then \(I=\frac{100\times 10^{3}}{12000}\text{ A}\approx8.33\text{ A}\).

Step2: Calculate the power loss

The power loss formula is \(P_{loss}=I^{2}R\). Assume the length of the transmission line \(L = 100\text{ km}=10^{5}\text{ m}\) and \(R=
ho L\) (where \(
ho = 10^{-6}\Omega/\text{m}\)). So \(R = 10^{-6}\times10^{5}\Omega = 0.1\Omega\). Then \(P_{loss}=(8.33)^{2}\times0.1\text{ W}\approx7\text{ W}\)

Answer:

7 W