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.
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(1−e−tRL1)⇒1−e−tRL=12⇒t1RL=In2Again14LE2R2=12LE2R2(1−e−tRL)2⇒e−tRL2=√2−1√2=2−√22⇒t1=τIn(12−√2)+in2So,t2−t1=τIn12−√2