A coil of inductance 1 H and resistance 100 Ω is connected to a… | JEE Main 2022 (29 Jul, Shift 1)

Q7JEE Main 2022 · 29 JUL · SHIFT 1Easy

Inductors & DC Transients (Mixed)

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 $\ln 2 = 0.693,\ e^{-3/2} = 0.25$ )

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Answer: (c)

$\tau = \frac{L}{R} = \frac{1}{100} = 10\text{ ms}$ , $i = i_0(1 - e^{-t/\tau})$ with $i_0 = \frac{6}{100} = 0.06\text{ A}$ .
Half value: $e^{-t/\tau} = \frac{1}{2} \Rightarrow t = \tau\ln 2 = 10 \times 0.693 \approx 7\text{ ms}$
At $t = 15\text{ ms}$ : $i = 0.06(1 - e^{-3/2}) = 0.06 \times 0.75 = 0.045\text{ A}$
$U = \frac{1}{2}Li^2 = \frac{1}{2}(1)(0.045)^2 \approx 1\times10^{-3}\text{ J}$
So the answer is (c) t = 7 ms; U = 1 mJ.

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Inductors & DC Transients (Mixed) question from JEE Main 2022 (29 Jul, Shift 1)

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