KCET · Physics · Current Electricity
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 \(I R t\)
- D \(I^2 R t\)
Answer & Solution
Correct Answer
(D) \(I^2 R t\)
Step-by-step Solution
Detailed explanation
The given situation is shown in the diagram.
In time \(t\), work done by the battery to establish the current \(I\) is given as.
\(\begin{aligned} W & =V q=V I t & {[\because q=I t] } \\ & =I R \cdot I t & {[\because V=I R] } \\ & =I^2 R t & \end{aligned}\)
In time \(t\), work done by the battery to establish the current \(I\) is given as.
\(\begin{aligned} W & =V q=V I t & {[\because q=I t] } \\ & =I R \cdot I t & {[\because V=I R] } \\ & =I^2 R t & \end{aligned}\)
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