Question

A solenoid of $10$ henry inductance and $2$ ohm resistance, is connected to a $10$ volt battery. In how much the magnetic energy will be increases to $1/4th$ of the maximum value?

• A. $3.5sec$
• B. $2.5sec$
• C. $5.5sec$
• D. $7.5sec$

Answer 1

The correct option is A $3.5sec$

Given,

$R=2\Omega$

$L=10H$

Let $I_0$ be the maximum current and $I$ be the current when the energy is $\frac{1}{4}$th of the maximum value.

$\frac{1}{2}L{I}^2=\frac{1}{4}(\frac{1}{4}L{I}_0^2$)

$I=\frac{I_0}{2}$

As we know,

$I=I_0(1-e^{\frac{-Rt}{L}})$

$e^{\frac{-Rt}{L}}=1-\frac{I}{I_0}=\frac{1}{2}$

Applying log

$\frac{-Rt}{L}=log0.5$

$\frac{Rt}{L}=0.693$

$t=0.693\times \frac{10}{2}=3.465sec\approx 3.5sec$