In the given circuit,the switch is in positio | vedclass

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

Question

(A) The time constant $	au$ for an $RL$ circuit is given by $	au = \frac{L}{R_{eq}}$.When the switch is in position $a$,the inductor $L = 4\,mH$ is

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) The time constant $	au$ for an $RL$ circuit is given by $	au = \frac{L}{R_{eq}}$.When the switch is in position $a$,the inductor $L = 4\,mH$ is in series with the parallel combination of resistors $R$ and $500\,\Omega$.The equivalent resistance $R_{eq}$ is the resistance seen by the inductor,which is $R_{eq} = \frac{R 	imes 500}{R + 500}$.Given $	au = 10\,\mu s = 10 	imes 10^{-6}\,s$ and $L = 4\,mH = 4 	imes 10^{-3}\,H$.Substituting these values into the formula:$10 	imes 10^{-6} = \frac{4 	imes 10^{-3}}{\left(\frac{R 	imes 500}{R + 500}ight)}$$10 	imes 10^{-6} = \frac{4 	imes 10^{-3} 	imes (R + 500)}{500R}$$10^{-5} = \frac{4 	imes 10^{-3} 	imes (R + 500)}{500R}$$500R 	imes 10^{-5} = 4 	imes 10^{-3} 	imes (R + 500)$$5 	imes 10^{-3} R = 4 	imes 10^{-3} R + 2000 	imes 10^{-3}$$10^{-3} R = 2$$R = 2000\,\Omega = 2\,K\Omega$.

In the given circuit,the switch is in position $a$. For what value of $R$ will the circuit have a time constant of $10\,\mu s$ in $K\Omega$?

Similar Questions

An inductor coil stores $U$ energy when $I$ current is passed through it and dissipates energy at the rate of $P$. The time constant of the circuit,when this coil is connected across a battery of zero internal resistance,is

An induction coil stores $32 \ J$ of magnetic energy and dissipates energy as heat at the rate of $320 \ W$ when a current of $4 \ A$ is passed through it. Find the time constant of the circuit when the coil is joined across a battery.

If $L$ is the inductance and $R$ is the resistance,then the $SI$ unit of $\frac{L}{R}$ is

An inductor coil carries a steady-state current of $2.0 \ A$ when connected across an ideal battery of $emf$ $4.0 \ V$. If its inductance is $1.0 \ H$,find the time constant of the circuit in $sec$.

Two figures are shown as Fig. $A$ and Fig. $B$. The time constant of Fig. $A$ is $\tau_{A}$ and the time constant of Fig. $B$ is $\tau_{B}$. Then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module