Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A coil of inductance 300 mH and resistance  is connected to a source of voltage

A coil of inductance 300 mH and resistance \mathrm{2\Omega } is connected to a source of voltage 2V. The current reaches half of its steady state value in:

Option: 1

0.05 s


Option: 2

0.1 s


Option: 3

0.15 s


Option: 4

0.3 s


Answers (1)

best_answer

The current at any instant is given by

\mathrm{\begin{aligned} & \Rightarrow I=I_0\left(1-e^{-R t / L}\right) \\ & \Rightarrow \frac{I_0}{2}=I_0\left(1-e^{-R t / L}\right) \\ & \text { or } \quad \frac{1}{2}=\left(1-e^{-R t / L}\right) \end{aligned}}

\mathrm{or \; \mathrm{e}^{-\mathrm{Rt} / \mathrm{L}}=\frac{1}{2}}

\mathrm{\begin{aligned} & \text { or } \frac{R t}{L}=\ln 2 \\ & \therefore \quad t=\frac{L}{R} \ln 2=\frac{300 \times 10^{-3}}{2} \times 0.693=150 \times 0.693 \times 10^{-3}=0.10395 \mathrm{~s}=0.1 \mathrm{~s} \end{aligned} }

Posted by

Anam Khan

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question