Chapter 37, Problem 16A

Why is it advantageous to transmit electric power long distances at high voltages?

To determine

To explain: The advantages of transmitting electric power through long distances at high voltages.

Explanation of Solution

Introduction:

Power loss in transmitting wires is inversely proportional to voltage.

Let power P be delivered via transmission lines or cable having resistance R.

Let V be the voltage and I be the current at which power is delivered.

Hence, $P=VI\Rightarrow I=\frac{P}{V}$

Power dissipated in transmission cables is denoted by $P_C$ . It is given by,

  $\begin{array}{l}{P}_C=I^{2}R\\ P_C={\left(\frac{P}{V}\right)}^{2}R\\ P_C=\frac{P^{2}R}{V^2}\\ P_C\propto \frac{1}{V^2}\end{array}$

Conclusion:

Power loss through transmission cables $P_C$ is inversely proportional to $V^2$ . By transmitting at high voltages, power loss in transmission cables is minimized.