A wire of resistance $R$ is connected across a cell of emf $(\varepsilon)$ and internal resistance $(r)$. The current through the circuit is $I$. In time $t$, the work done by the battery to establish the current $I$ is

• A

  EIt
• B

  $\frac{\varepsilon^2 t}{R}$
• C

  $I R t$
• Correct answer
  D

  $I^2 R t$

Solution

The given situation is shown in the diagram. In time $t$, work done by the battery to establish the current $I$ is given as.
$\begin{aligned} W & =V q=V I t & {[\because q=I t] } \\ & =I R \cdot I t & {[\because V=I R] } \\ & =I^2 R t & \end{aligned}$

Hence, the correct answer is option: 'D'.