Question

In an $LR$ circuit connected to a battery, the rate at which energy is stored in the inductor is plotted against time during the growth of the current in the circuit. Which of the following curves best represents the resulting curve?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

In $LR$ circuit during growth of current, energy stored at a particular instant is given by,

$U=\frac{1}{2}L{i}^2$

So, the rate at which energy is stored in the inductor,

$\frac{\Delta U}{\Delta t}=\frac{1}{2}L\left(2i\right)\left(\frac{\Delta i}{\Delta t}\right)=Li\left(\frac{\Delta i}{\Delta t}\right)$

At $t=0$,

$i=0\Rightarrow \frac{\Delta i}{\Delta t}=0\Rightarrow \frac{\Delta U}{\Delta t}=0$

At $t=\infty$,

$i=i_0\left(\text{maximum constant value}\right)\Rightarrow \frac{\Delta i}{\Delta t}=0\Rightarrow \frac{\Delta U}{\Delta t}=0$

This is only best represented by the curve in option $\left(A\right)$.