Question

Define electric power. Express it in terms of potential difference $V$ and resistance $R$.

Answer 1

Hint:Joules law of heating shows the electrical power equation relation to the current, by using the Joule's law equation and the ohm's law equation the electric power in terms of the potential difference $V$ and the resistance $R$ can be determined.

Useful formula:
Joule’s law of heating,
$P = {I^2}R$
Where, $P$ is the electric power of the circuit, $I$ is the current in the circuit in ampere and $R$ is the resistance in the circuit in ohms.
Ohms law shows,
$V = IR$
Where, $V$ is the potential difference in the circuit, $I$ is the current in the circuit in ampere and $R$ is the resistance in the circuit in ohms.

Complete step by step solution:
Joule’s law of heating,
$P = {I^2}R\,.......................\left( 1 \right)$
Ohm's law,
$V = IR\,.................\left( 2 \right)$
In equation (2), the current is written as,
$I = \dfrac{V}{R}\,..............\left( 3 \right)$
Now substituting the above equation (3) in the equation (1), then the equation (1) is written as,
$P = {\left( {\dfrac{V}{R}} \right)^2}R\,$
Now squaring the terms in the above equation, then the above equation is written as,
$P = \left( {\dfrac{{{V^2}}}{{{R^2}}}} \right) \times R\,$
On multiplying the above equation, then the above equation is written as,
$P = \dfrac{{{V^2} \times R}}{{{R^2}}}$
On cancelling the resistance in numerator and in the denominator, then the above equation is written as,
$P = \dfrac{{{V^2}}}{R}$
Thus, the above equation shows the relation between the power, potential difference and resistance.

Hence, the electric energy is derived in terms of the potential difference and resistance.

Note:In physics, an electric power measure of the rate of electrical energy transfer by an electric circuit per unit time. Denoted by $P$ and measured using the SI unit of power is the watt or one joule per second. Electric power is commonly supplied by sources such as electric batteries and produced by electric generators.