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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 $\frac{L\varepsilon^2}{8R^2}$.

Vedclass · Answer

(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?

Similar Questions

The current in an $LR$ circuit builds up to $3/4$ of its steady state value in $4 \, s$. The time constant of this circuit is:

In the circuit shown,an inductor $L$ and a capacitor $C$ are connected as shown. $A_1$ and $A_2$ are ammeters. When the key $K$ is pressed to complete the circuit,what will be the readings of $A_1$ and $A_2$ just after closing the key $K$?

$Henry/ohm$ can be expressed in

Find the current in the sliding rod $AB$ (resistance $= R$) for the arrangement shown in the figure. The magnetic field $\vec{B}$ is constant and directed out of the paper. The parallel wires have no resistance,and the velocity $v$ is constant. The switch $S$ is closed at time $t = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module