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:

Magnetic energy in a solenoid is given byU=12LI021−e−RtL2 ⇒U=U01−e−RtL2      ∵U0=12LI02⇒25U0100=U01−e−RTL2 ⇒12=1−e−RtL⇒2=eRtL Applying logarithm on both sides⇒ ln⁡2=RtL ⇒ t=LRln⁡2