Question

If an electrical appliance of $R\Omega$ resistance draws a current ‘I’ for time ‘t’ and connected across a battery of potential V then, which among the following does not help you calculate the energy consumed by the appliance.

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

Answer 1

The correct option is D $V^{2}Qt$

Energy dissipated = work done = Power $\times$ time
Work done for a charge q to move in a potential difference V is$q\times V$
Power = Work done per unit time $=\frac{q\times V}{t}$
$\therefore Power=VI(I=\frac{q}{t})$
$\therefore$ Energy dissipated = VIt (Power = VI)
Energy dissipated $=I^{2}Rt(V=IR)$
Energy dissipated $=\frac{V^2}{R}t(I=\frac{V}{R})$

In terms of charge, power can be written as $P=VIt=V\times \frac{Q}{t}\times t=VQ$