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Question

A coil having an inductance L and a resistance R is connected to a battery of emf ε Find the time taken for the magnetic energy stored in the circuit to change from one fourth of th steady - state to half of the steady state value.

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Solution

Maximum current =ER
In stead state magnetic field energy stored
=E22R2L
The fourth of steady state energy
=18LE2R2
One half steady energy =14LE2R2
18LE2R2=12LE2R2(1etRL1)1etRL=12t1RL=In2Again14LE2R2=12LE2R2(1etRL)2etRL2=212=222t1=τIn(122)+in2So,t2t1=τIn122


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