Question

Which of the following expressions represent(s) the electrical power in a circuit?
(V - Potential difference, I - current and R - Resistance)

• A. I²R
• B. IR²
• C. VI
• D. V²/R

Answer 1

Answer: (A), (C), (D)

The correct options are
A

I²R

C

VI

D

V²/R

Electrical power is the rate at which electrical energy is supplied by a source which is equal $\frac{\text{energy supplied (W)}}{\text{time (t)}}$.

The electrical energy W supplied by a source in providing a current I for time t in a conductor under a potential difference V is given by W = VIt.

So, $\text{P}=\frac{\text{VIt}}{\text{t}}$ = VI

By Ohm's law, $\text{V = IR or I =}\frac{\text{V}}{\text{R}}$ (Where R is the resistance)

Substituting the value of I in the expression of power, $\text{P = VI = V.}\frac{\text{V}}{\text{R}}=\frac{{\text{V}}^2}{\text{R}}$

Since $\text{V = IR, P =}\frac{{\text{V}}^2}{\text{R}}=\frac{{\text{(IR)}}^2}{\text{R}}={\text{I}}^2\text{R}$

Thus electrical power = $\frac{\text{W}}{\text{t}}=\text{VI}=\frac{{\text{V}}^2}{\text{R}}={\text{I}}^2\text{R}$