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

An emf of $15 V$ is applied to a circuit containing $5 H$ inductance and $10 \Omega$ resistance. The ratio of currents at time $t=\infty$ and $t=1 s$ after closing the switch is:

When a $DC$ voltage is applied at the two ends of a circuit kept in a closed box, it is observed that the current gradually increases from zero to a certain value and then remains constant. What do you think the circuit contains?

The current $(i)$ at time $t = 0$ and $t = \infty$ respectively for the given circuit is

When a battery is connected across a series combination of self inductance $L$ and resistance $R$,the variation in the current $i$ with time $t$ is best represented by

Two resistors of $10 \Omega$ and $20 \Omega$ and an ideal inductor of $10 \ H$ are connected to a $2 \ V$ battery as shown. The key $K$ is closed at time $t=0$. Find the initial $(t=0)$ and final $(t \rightarrow \infty)$ currents through the battery.

Vedclass Test Series

Exam Paper Generator

Online Exam Module