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Q.

A coil of inductance 1 H and resistance 10Ω is connected to a resistanceless battery of emf 50 V at time t= 0 Calculate the ratio of the rate at which magnetic energy is stored in the coil to the rate at which energy is supplied by the battery at $t = 0 .1 s .$

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answer is 0.37.

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Detailed Solution

$τ_{L} = \frac{L}{R} = 0 .1 s$
The given time $t = 0 .1 s is one time constant$
The desired ratio is $\frac{{iV}_{L}}{iE}$ $(∵ P = Vi) a$
$= \frac{V_{L}}{E}$
After on time constant $V_{L} = \frac{E}{e} as$

Hence, the desired ratio is $\frac{1}{e} \approx 0 .37$ .

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