Chapter 18, Problem 11Q

To determine

To explain:

The reason how the transfer of electric power at very high voltages, over large distances helps to save power losses

Answer to Problem 11Q

Solution:

When voltage is heavily increased, the current decreases and thus Joule heating reduces in the transmission lines.

Explanation of Solution

Formula used:

    • The Ohm’s law tells that the ratio of voltage drop (V)and the current (I)passing through a resistance (R)is ideally constant which is equal to the value of that resistance itself, i.e.,

             $R=\frac{V}{I}$

    • The power consumption by a resistor is given as,

             $P=I^{2}R=V\times I=\frac{V^2}{R}$

Ideally, the transmission lines are assumed to have zero resistance, but practically for the long distances it is not correct. When electric power is transferred over large distances, the transmission lines offer substantial amount of resistance. So, an undesired power loss $\left(P=I^{2}R\right)$ is offered by the transmission line. It is called, line-loss.

For a power generating company, it becomes highly important to reduce this line-loss without any change in the power supplied and received at house-holds. From the formula $P=I^{2}R$, we can say that this line-loss can be reduced by decreasing the current in the line.

So, from the formula $P=V\times I$, we can say that for a constant power supply from the company, if the voltage is highly increased, the current will highly decrease. Thus, the line-loss $\left(P=I^{2}R\right)$, offered by the transmission line will also heavily decrease.