For L-R circuit,the time constant is equal to | vedclass

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

Question

(A) In an $L-R$ circuit,the energy stored in the magnetic field of the inductor is given by $U = \frac{1}{2} L I^2$.The rate of energy dissipation in

Vedclass · Accepted Answer

twice the ratio of the energy stored in the magnetic field to the rate of the dissipation of energy in the resistance.

Vedclass · Answer

(A) In an $L-R$ circuit,the energy stored in the magnetic field of the inductor is given by $U = \frac{1}{2} L I^2$.The rate of energy dissipation in the resistor is given by $P = I^2 R$.The ratio of the energy stored to the rate of dissipation is $\frac{U}{P} = \frac{\frac{1}{2} L I^2}{I^2 R} = \frac{1}{2} \frac{L}{R}$.Since the time constant $	au$ is defined as $	au = \frac{L}{R}$,we have $\frac{U}{P} = \frac{1}{2} 	au$.Therefore,$	au = 2 	imes \frac{U}{P}$,which means the time constant is twice the ratio of the energy stored in the magnetic field to the rate of dissipation of energy in the resistance.

For $L-R$ circuit,the time constant is equal to

Similar Questions

Switch $S$ of the circuit shown in the figure is closed at $t = 0$. If $e$ denotes the induced $emf$ in $L$ and $i$ the current flowing through the circuit at time $t$,which of the following graphs is correct?

Three identical resistors with resistance $R = 12\,\Omega$ and two identical inductors with self-inductance $L = 5\,mH$ are connected to an ideal battery with an emf of $12\,V$ as shown in the figure. The current through the battery long after the switch has been closed will be $......A$.

$A$ resistor of $20 \, \Omega$ and an inductor of $5 \, H$ are connected in series with a $5 \, V$ battery. What is the rate of change of current at $t = 0.25 \, s$?

An inductor coil stores $64 \, J$ of magnetic field energy and dissipates energy at the rate of $640 \, W$ when a current of $8 \, A$ is passed through it. If this coil is joined across an ideal battery,find the time constant of the circuit in seconds.

The current growth in two $L-R$ circuits $(b)$ and $(c)$ is shown in figure $(a)$. Let $L_1, L_2, R_1$ and $R_2$ be the corresponding values in the two circuits. Then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module