Question

The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R, inductance L is connected to a battery, is :

(1) \(\frac LR{ln}5\)

(2) infinite

(3) \(\frac LR{ln2}\)

(4) \(\frac LR{ln10}\)

Answer 1

Correct option is (3) \(\frac LR{ln2}\) 

Magnetic energy = \(\frac 12\)Li² = 25%

ME ⇒ 25% ⇒ i = \(\frac{i_0}2\)

i = i₀(1 - R^-Rr/L) for charging

t = \(\frac LR{ln2}\)