Chapter 25 Problem 35

Problem

An electric power plant can produce electricity at a fixed power $P$, but the plant operator is free to choose the voltage $V$ at which it is produced. This electricity is carried as an electric current $I$ through a transmission line (resistance $R$) from the plant to the user, where it provides the user with electric power $P^{\prime }$

(a) Show that the reduction in power $\Delta P=P-P^{\prime }$ due to transmission losses is given by

$\Delta P=P^{2}R{\big /}V^{2}$

(b) In order to reduce power losses during transmission, should the operator choose $V$ to be as large or as small as possible?