Question

Power is the amount of energy transferred or converted per unit time. Transmission lines transmit a voltage of V volt to our houses from power stations, then the power P supplied by them is proportional to:
a. $\dfrac{1}{V}$
b. $V$
c. ${V^2}$
d. $\dfrac{1}{{{V^2}}}$

Answer 1

Hint: We know that for the formula of power is given by the formula,
$P = V \times I$
Where P = Power in watt
V = Voltage in volt
I = Current in ampere
By the formula it is cleared that power is directly proportional to the voltage and current flowing through of the wire.

Complete step by step solution :
According to the definition of power in an electric circuit the power is defined as the rate of heat dissipation (work done) per second when the electricity transfers from one place to another.
$power = \dfrac{{work}}{{time}}$

And we know that the work done in flow of electricity is given by
$W$ = $\dfrac{{{V^2}}}{R}T$

For the calculation of power,
$\therefore$ $P = \dfrac{W}{T}$

$P = \dfrac{{\dfrac{{{V^2}}}{R}T}}{T}$

$P = \dfrac{{{V^2}}}{R} \cdot \cdot \cdot \cdot \cdot \cdot \left( 1 \right)$

By ohm’s law
$V = I \times R \Leftrightarrow R = \dfrac{V}{I} \cdot \cdot \cdot \cdot \cdot \cdot (2)$

From (1) and (2) we get
$P = V \times I$

Hence the power (P) is directly proportional to the voltage (V) i.e.
$P \propto V$

Hence the correct option is B.

Note: The other formula of power are as follows :
$P = \dfrac{{{V^2}}}{R}$
$P = {I^2}R$
These formulae have been not used because in our home circuit both current as well as current varies according to the relation,
$P = V \times I$
In order to maintain the power supply to remain constant one of them may increase and another one decreases according to load resistance.