In the given L-R circuit,which of the followi | vedclass

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(A) For an $L-R$ circuit connected to a $DC$ source $\varepsilon$,the Kirchhoff's voltage law equation is $\varepsilon = L \frac{dI}{dt} + IR$.The ene

Vedclass · Accepted Answer

The magnitude of the rate of change of current is $\frac{\varepsilon}{2L}$ when the energy stored in the inductor is $\frac{L\varepsilon^2}{8R^2}$.

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(A) For an $L-R$ circuit connected to a $DC$ source $\varepsilon$,the Kirchhoff's voltage law equation is $\varepsilon = L \frac{dI}{dt} + IR$.The energy stored in the inductor is given by $U = \frac{1}{2} LI^2$.For option $A$,the energy is $U = \frac{L\varepsilon^2}{8R^2}$.Equating this to $\frac{1}{2} LI^2$,we get $\frac{1}{2} LI^2 = \frac{L\varepsilon^2}{8R^2}$,which simplifies to $I^2 = \frac{\varepsilon^2}{4R^2}$,so $I = \frac{\varepsilon}{2R}$.Substituting $I$ into the circuit equation: $\varepsilon = L \frac{dI}{dt} + (\frac{\varepsilon}{2R})R = L \frac{dI}{dt} + \frac{\varepsilon}{2}$.This gives $L \frac{dI}{dt} = \frac{\varepsilon}{2}$,or $\frac{dI}{dt} = \frac{\varepsilon}{2L}$.Thus,option $A$ is correct.

In the given $L-R$ circuit,which of the following statements is correct?

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