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

JEE Main · 2005 · 08 May 2005 · Offline · Electromagnetic Induction

A coil of inductance 300 mH and resistance

2Ω

is connected to a source of voltage 2 V. The current reaches half of its steady state value in

(A)0.05 s
(B)0.1 s✓ Correct
(C)0.15 s
(D)0.3 s

Answer: (B)

Solution

In the growing

L R

circuit

I = I_{0} (1 - e^{- R t / L})

. Reaching half the steady value needs

e^{- R t / L} = \frac{1}{2}

, so

\frac{R t}{L} = ln 2

and

t = \frac{L l n 2}{R} = \frac{0.3 \times 0.693}{2} \approx 0.1

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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