Question

An inductance L and a resistance R are first connected to a battery. After some time the battery is disconnected but L and R remain connected in a closed circuit. Then the current reduces to $37\%$ of its initial value in:

• A. RL sec
• B. $\frac{R}{L}$ sec
• C. $\frac{L}{R}$ sec
• D. $\frac{1}{LR}$ sec

Answer 1

The correct option is C $\frac{L}{R}$ sec

$I=I_0{e}^{\frac{-t}{\tau }}$

$\tau =$ time constant.

$I_0=$ initial maximum current.

When $I=37\%$ of $I_0$

$I=0.37I_0$

$e^{\frac{-t}{\tau }}=0.37$

$\frac{t}{\tau }=1$

$t=T=\frac{L}{R}sec$