Question

If an electrical appliance of $\text{R}\Omega$ resistance draws a current $\text{I}$ for time $\text{t}$, and is connected across a battery of potential $\text{V}$, then the energy consumed by the appliance is:

• A. $\frac{{\text{V}}^2\text{R}}{\text{t}}$
• B. ${\text{I}}^2\text{Rt}$
• C. $\text{VIt}$
• D. $\frac{{\text{V}}^2\text{t}}{\text{R}}$

Answer 1

Answer: (B), (C), (D)

$\frac{{\text{V}}^2\text{t}}{\text{R}}$

Work done in moving a charge $\text{q}$ in a potential difference $\text{V}$ is $\text{qV}$.
Power = Work done per unit time $=\frac{\text{qV}}{\text{t}}$ = $\text{VI}$, as current $\text{I}=\frac{\text{q}}{\text{t}}$

Energy consumed = Power consumed $\times$ Time = $\text{VIt}$ $\to$ (1)

From ohm's law, $\text{V = IR}$ $\to$ (2)

$⟹\text{I}=\frac{\text{V}}{\text{R}}$ $\to$ (3)

From (1) & (2), Energy consumed = $\text{IR}\times \text{It}={\text{I}}^2\text{Rt}$

From (1) & (3), Energy consumed = $\text{V}\times \frac{\text{V}}{\text{R}}\text{t}=\frac{{\text{V}}^2\text{t}}{\text{R}}$