In the LR circuit shown,what is the variation | vedclass

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

Question

(C) Let $I_1$ be the current through the inductor $L$ and $I_2$ be the current through the resistor $R$ in the middle branch. The current $I$ flows th

Vedclass · Accepted Answer

$-\frac{V}{R}\,\,{e^{ - \,\frac{{Rt}}{L}}}$

Vedclass · Answer

(C) Let $I_1$ be the current through the inductor $L$ and $I_2$ be the current through the resistor $R$ in the middle branch. The current $I$ flows through the top branch containing the $2V$ battery.Applying Kirchhoff's loop law for the loop $CDE$ (top loop): $-2V + V + I_2 R = 0 \implies I_2 = \frac{V}{R} \dots(1)$Applying Kirchhoff's loop law for the outer loop $ABCDE$:$3V - I_1 R - L \frac{dI_1}{dt} - 2V = 0$$L \frac{dI_1}{dt} + I_1 R = V$This is a standard $LR$ circuit equation. The solution for $I_1$ is:$I_1(t) = \frac{V}{R} (1 - e^{-Rt/L}) \dots(2)$Applying Kirchhoff's junction law at node $C$:$I_1 = I + I_2$$I = I_1 - I_2 = \frac{V}{R} (1 - e^{-Rt/L}) - \frac{V}{R}$$I = -\frac{V}{R} e^{-Rt/L}$

In the $LR$ circuit shown,what is the variation of the current $I$ as a function of time? The switch is closed at time $t = 0 \, s.$

Similar Questions

The magnetic field in the region shown in the figure increases at a constant rate of $20 \, mT/sec$. Each side of the square loop $ABCD$ has a length of $1 \, cm$ and a resistance of $4 \, \Omega$. Find the current in the wire $AB$ if the switch $S$ is closed.

Near a circular loop of conducting wire as shown in the figure,an electron moves along a straight line. The direction of the induced current,if any,in the loop is

An electron is moving in a circular orbit of radius $R$ with an angular acceleration $\alpha$. At the centre of the orbit is kept a conducting loop of radius $r$ $(r \ll R)$. The $e.m.f.$ induced in the smaller loop due to the motion of the electron is

The bob of a simple pendulum is replaced by a magnet. The oscillations are set along the length of the magnet. $A$ copper coil is added so that one pole of the magnet passes in and out of the coil. The coil is short-circuited. Then which one of the following happens?

Consider the conducting square loop shown in the figure. If the switch is closed and after some time it is opened again,then the square loop will show:

Vedclass Test Series

Exam Paper Generator

Online Exam Module