(C) The current in an $LR$ circuit is given by $i = \frac{E}{R}(1 - e^{-t/\tau})$,where $\tau = \frac{L}{R} = \frac{1}{100} = 0.01\,s = 10\,ms$.$(a)$

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

(C) The current in an $LR$ circuit is given by $i = \frac{E}{R}(1 - e^{-t/\tau})$,where $\tau = \frac{L}{R} = \frac{1}{100} = 0.01\,s = 10\,ms$.$(a)$ For the current to reach half its steady-state value $(i = \frac{E}{2R})$:$\frac{E}{2R} = \frac{E}{R}(1 - e^{-t/\tau})$$0.5 = 1 - e^{-t/\tau} \implies e^{-t/\tau} = 0.5$$t = \tau \ln 2 = 10\,ms \times 0.693 = 6.93\,ms \approx 7\,ms$.$(b)$ At $t = 15\,ms$,$t/\tau = 15/10 = 1.5$:$i = \frac{6}{100}(1 - e^{-1.5}) = 0.06(1 - 0.25) = 0.06 \times 0.75 = 0.045\,A$.The energy stored is $U = \frac{1}{2}Li^2 = \frac{1}{2} \times 1 \times (0.045)^2 = 0.5 \times 0.002025 \approx 0.001\,J = 1\,mJ$.

Class 12 Physics Electromagnetic Induction R-L D.C. Circuit

Difficult

$A$ coil of inductance $1\,H$ and resistance $100\,\Omega$ is connected to a battery of $6\,V$. Determine approximately:
$(a)$ The time elapsed before the current acquires half of its steady-state value.
$(b)$ The energy stored in the magnetic field associated with the coil at an instant $15\,ms$ after the circuit is switched on. (Given $\ln 2 = 0.693$,$e^{-3/2} = 0.25$)

JEE MAIN 2022 All JEE MAIN

A
$t = 10\,ms; U = 2\,mJ$
B
$t = 10\,ms; U = 1\,mJ$
C
$t = 7\,ms; U = 1\,mJ$
D
$t = 7\,ms; U = 2\,mJ$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Physics Questions

Chapter

Electromagnetic Induction

Subtopic

R-L D.C. Circuit

Previous Year

JEE MAIN 2022 Paper All JEE MAIN years →

$A$ 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 $t = 0.25 \, s$?

Medium

View Solution

The figure shows a circuit that contains three resistors with resistance $R = 2.0 \, \Omega$, two inductors with inductance $L = 2.0 \, mH$, and an ideal battery with $emf$ $E = 9 \, V$. The current $i$ just after the switch $S$ is closed will be .... $A$.

DifficultJEE MAIN 2021

View Solution

In the figure,a lamp $P$ is in series with an iron-core inductor $L$. When the switch $S$ is closed,the brightness of the lamp rises relatively slowly to its full brightness compared to the case without the inductor. This is due to:

Medium

View Solution

An inductor $(L = 100 \, mH)$,a resistor $(R = 100 \, \Omega)$ and a battery $(E = 100 \, V)$ are initially connected in series as shown in the figure. After a long time,the battery is disconnected by short-circuiting the points $A$ and $B$. The current in the circuit $1 \, ms$ after the short circuit is

Difficult

View Solution

An inductor $L$,a resistance $R$,and two identical bulbs $B_1$ and $B_2$ are connected to a battery through a switch $S$ as shown in the figure. The resistance $R$ is the same as that of the coil that makes $L$. Which of the following statements gives the correct description of the happenings when the switch $S$ is closed?

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

$A$ 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 $t = 0.25 \, s$?

The figure shows a circuit that contains three resistors with resistance $R = 2.0 \, \Omega$, two inductors with inductance $L = 2.0 \, mH$, and an ideal battery with $emf$ $E = 9 \, V$. The current $i$ just after the switch $S$ is closed will be .... $A$.

In the figure,a lamp $P$ is in series with an iron-core inductor $L$. When the switch $S$ is closed,the brightness of the lamp rises relatively slowly to its full brightness compared to the case without the inductor. This is due to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module