Question

Define electric power. Write SI unit of power and derive the formula for power.

Answer 1

Step 1: Definition of electric power

The rate of transfer of electrical energy is termed electric power. The electric power is measured in watts which is its SI unit, and electric power is represented by W.

Step 2: Derivation of electric power
The formula for electric power in terms of the work done is given.

$\mathrm{Power},\mathrm{P}=\frac{\mathrm{Work}\left(W\right)}{\mathrm{time}\left(t\right)}$ ……. (1)

Here, work is in joules, and time is in seconds.

The formula for the potential difference is,

$V=\frac{W}{Q}$

Here, W is the work done, and Q is charge.

Rewrite the equation as,

$W=VQ$ ……. (2)

Substitute equation (2) in equation (1).

$P=\frac{VQ}{t}$

Since, the charge per unit time is current $I=\frac{Q}{t}$, rewrite the equation as,

$P=VI$ …….. (3)

Step 4: Determine the formula for electric power in terms of resistance $\mathrm{R}$ and current $\mathrm{I}$.

Consider the formula for Ohm's law.

$V=IR$

Substitute the above equation in equation (3).

$\begin{array}{rcl}P& =& \left(IR\right)I\\ & =& I^{2}R\end{array}$

Step 5: Determine the formula for electric power in terms of potential difference $V$ and resistance $R$.

Rewrite the formula for Ohm's law.

$I=\frac{V}{R}$

Substitute the above expression in equation (3).

$\begin{array}{rcl}P& =& V\left(\frac{V}{R}\right)\\ & =& \frac{V^2}{R}\end{array}$

Therefore, for all the formulas for power is,

$$\begin{gathered} P=\frac{W}{t} \\ P=\frac{VQ}{t} \\ P=VI \\ P=I^{2}R \\ P=\frac{V^2}{R} \end{gathered}$$