Question

Derive the formula P = VI of electric power.

Answer 1

Step 1: To prove

$P=VI$

Step 2: formula used

$$\begin{gathered} Vispotentialdifference \\ Iiscurrent \\ tistime \\ UisEnergy \\ Qischarge \end{gathered}$$

Power is equal to the rate of consumption of electrical energy

Step 3: Derivation

$$\begin{gathered} P=U/t \\ U=V.dQ \\ P=(V.dQ)/dt \\ P=V.dQ/dt\dots ..\left(1\right) \end{gathered}$$

As we know, the current is equal to the rate of change of electric charge.

So, $I=dQ/dt$

Therefore, putting the value of dQ/dt in equation 1, we get;

$P=VI$

Hence, electric power, $P=VI$