Question

The power dissipated in a transmission wire carrying current I and voltage V is inversely proportional to :
(A) V
(B) \[{V^2}\]
(C) \[\sqrt V \]
(D) \[\sqrt I \]
(E) I

Answer 1

Hint Power transmitting through an electrical wire is given by \[P = VI\] , power responsible for heat effect or power loss is given by \[{P_H} = {I^2}R\] . Substitute this in the earlier equation. From this we know that power is inversely proportional to the square of the voltage.

Complete step-by-step solution
As we know that the power transmitted through an electrical wire is given as:
 \[P = VI\] --1
And in this wire, the current is sole responsible for the production of heat,
 \[{P_H} = {I^2}R\] --2
Substituting 1 in 2 we get,
 \[{P_H} = {(\dfrac{P}{V})^2}R\] ,
 Therefore, when the voltage decreases by a factor, power will increase by the square of that factor,
Here we can we that, power lost in transmission is inversely proportional to \[{V^2}\]

Therefore, the correct answer is option B

Note Power lost solely depends on the electric current passing through it, that’s the same reason why wire coming to our home from a nearby station is ramped up to such a high voltage. It is done to minimize current and maximize voltage to reduce the energy lost as heat between 2 points