Question

In the transmission of A.C power through transmission lines, when the voltage is shaped up n times, the power loss in transmission,
(A) increases n times
(B) decreases n times
(C) increase ${n^2}$ times
(D) decrease ${n^2}$ times

Answer 1

Hint: In order to solve this question, we will first find the value of current in terms of power and voltage, and then using the general power loss formula we will find the dependency of power loss with the voltage when voltage is changed by n times.

Formula used:
Power loss in an A,C transmission is calculated using formula $P = {I^2}R$ and input power is calculated using $P' = VI$ where, V is the voltage of the source, I is the current flowing, and R is the resistance.

Complete answer:
We have given that In the transmission of A.C power through transmission lines when the voltage is shaped up n times we need to find the dependency of power loss with n. Now, let initial power loss when input voltage is V is given by $P = {I^2}R \to (i)$ and we can write the current in the form of voltage and input power using $P' = VI$ therefore, $I = \dfrac{{P'}}{V}$ put this value in equation (i) we get,
$P = {(\dfrac{{P'}}{V})^2}R$

Now since the voltage is increased by n times so the new voltage is ‘nV’ given by, so power loss is given by
$P = \dfrac{1}{{{n^2}}}{(\dfrac{{P'}}{V})^2}R$
so, power loss in inversely proportional to the ${n^2}$

Hence, the correct answer is option (D) decrease ${n^2}$ times.

Note: It should be remembered that current and resistance are kept the same it’s just voltage is changed and inversely proportional means when the value of n will increase the power loss will decrease by a factor of ${n^2}$ and its vice-versa for directly proportional quantities.