The time taken for the magnetic energy to reach 25 % of its maximum...

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 :

Options

A $\dfrac{L}{R}\ln 5$
Binfinite
C $\dfrac{L}{R}\ln 2$
D $\dfrac{L}{R}\ln 10$

Correct answer

C. $\dfrac{L}{R}\ln 2$

Step-by-step solution

Magnetic energy $= \dfrac{1}{2}L{i}^{2} = 25 %</p><p>$ ME ⇒ 25 % ⇒ i = \dfrac{{i}_{0}}{2} $</p><p>$ i = {i}_{0} $\left(1 - {R}^{- Rt / L}\right)$ for charging

$t = \dfrac{L}{R}\ln 2$

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