In the given figure, an inductor and a resistor are connected in… | JEE Main 2023 (13 Apr, Shift 1)

Q6JEE Main 2023 · 13 APR · SHIFT 1Difficult

Inductors & DC Transients (Mixed)

In the given figure, an inductor and a resistor are connected in series with a battery of emf E volt. $\frac{E^a}{2b}\text{ J/s}$ represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of $\frac{b}{a}$ will be __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 25

Rate of energy storage $P = \frac{d}{dt}\left(\frac{1}{2}Li^2\right) = Li\frac{di}{dt} = Ei - i^2R$
Maximum when $\frac{dP}{di} = E - 2iR = 0 \Rightarrow i = \frac{E}{2R}$ , giving $P_{max} = \frac{E^2}{4R}$
With $R = 25\ \Omega$ : $P_{max} = \frac{E^2}{100} = \frac{E^2}{2 \times 50}$ , so $a = 2$ , $b = 50$
$\frac{b}{a} = 25$

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