Electromagnetic Induction Part 1

The expression of the magnetic energy stored in the solenoid,
U=‌

LI2

2

The maximum value of the magnetic energy stored in the solenoid,
U0=‌

LI02

2

Given, U=25%×U0
⇒‌‌‌

LI2

2

=‌

1

4

×‌

LI02

2

⇒I=‌

I0

2

Therefore, using the formula for the decay current in L−R circuit,
I=I0(1−e−t∕τ)
‌

I0

2

=I0(1−e−2∕τ)
e−t∕τ=‌

1

2

⇒t=τ‌ln‌2
⇒t=‌

L

R

‌ln‌2