Chapter 21, Problem 80GP

To determine

To Prove:

The power loss in transmission lines, $P_L$ is given by $P_L={\left(P_T\right)}^2\frac{R_L}{V^2}$,where $P_T$ is the power transmitted to the user, V is the delivered voltage and $R_L$ is the resistance of the power lines.

Answer to Problem 80GP

Solution:

$P_L={\left(\frac{P_T}{V}\right)}^2{R}_L$.

Explanation of Solution

Given:

$\begin{array}{l}\text{power}\text{transmitted}\text{to}\text{the}\text{user}\text{is}{P}_T\\ \text{Resistence}\text{of}\text{power}\text{lines}{R}_L\\ \text{voltage}\text{delivered}\text{is}V\end{array}$

Formula Used:

$\begin{array}{l}\text{Current}\text{through }\text{the cable}I=\frac{P_T}{V}\\ \text{Power}\text{loss}\text{in}\text{the}\text{transmission}\text{cable}{P}_L=I^2{R}_L\end{array}$

Calculation:

$\begin{array}{l}\text{Current}\text{through }\text{the cable}I=\frac{P_T}{V}\\ \text{Power}\text{loss}\text{in}\text{the}\text{transmission}\text{cable}{P}_L=I^2{R}_L\\ \text{or}{P}_L={\left(\frac{P_T}{V}\right)}^2{R}_L\end{array}$