Question

When a steady current $I$ flows through a resistor of resistance $R$ under a constant potential difference $V$ for time $t$, the electrical work done by charge carrier is $W=$ ___________.

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

Answer 1

The correct option is D Any of these

Charge transported through the resistor in time $t$ is $q=It$
Work done by unit charge $=V$ (by definition)
$\therefore$Work done by charge, $q=Vq=VIt$
According to Ohm's law, $V=IR$
$W=VIt(V=IR)$
$=I^{2}Rt(V=IR)$
$=\frac{V^{2}t}{R}J(V^2=\frac{I^2{R}^2}{R}\times t)$