The ratio of the time constant in charging an | vedclass

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

Question

(B) When the switch is closed (charging),the inductor $L$ is in series with the resistor $2R$. The resistor $R$ is in parallel with the series combina

Vedclass · Accepted Answer

$3 : 2$

Vedclass · Answer

(B) When the switch is closed (charging),the inductor $L$ is in series with the resistor $2R$. The resistor $R$ is in parallel with the series combination of $2R$ and $L$. The time constant for the charging circuit is determined by the equivalent resistance $R_{eq}$ seen by the inductor. When the battery is shorted (or considered ideal),the equivalent resistance is $R_{eq} = 2R + R = 3R$. Thus,the charging time constant is $	au_{1} = \frac{L}{3R}$.When the switch is opened (discharging),the inductor $L$ forms a closed loop with the resistors $2R$ and $R$ in series. The total resistance in this loop is $R_{eq} = 2R + R = 3R$. Thus,the discharging time constant is $	au_{2} = \frac{L}{3R}$.Wait,re-evaluating the circuit: When the switch is closed,the inductor is in series with $2R$. The resistor $R$ is in parallel with the branch containing $2R$ and $L$. The effective resistance seen by the inductor is $R_{eq} = 2R + 0 = 2R$ (since the battery is ideal,the parallel branch $R$ does not affect the time constant). So $	au_{1} = \frac{L}{2R}$.When the switch is opened,the inductor discharges through the series combination of $2R$ and $R$. So $R_{eq} = 2R + R = 3R$. Thus,$	au_{2} = \frac{L}{3R}$.The ratio $\frac{	au_{1}}{	au_{2}} = \frac{L/2R}{L/3R} = \frac{3}{2}$.

The ratio of the time constant in charging and discharging in the circuit shown in the figure is

Similar Questions

In the circuit shown,the cell is ideal. The coil has an inductance of $4H$ and zero resistance. $F$ is a fuse of zero resistance and will blow when the current through it reaches $5A$. The switch is closed at $t = 0$. The fuse will blow after how much time?

An ideal coil of $10 \ H$ is connected in series with a resistance of $5 \ \Omega$ and a battery of $5 \ V$. $2 \ s$ after the connection is made,the current flowing in the circuit in amperes is:

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

In the circuit shown,$X$ is joined to $Y$ for a long time,and then $X$ is joined to $Z$. The total heat produced in $R_2$ is

In which of the following circuits is the current maximum just after the switch $S$ is closed?

Vedclass Test Series

Exam Paper Generator

Online Exam Module