Question

The time taken by the current to rise to $0.63$ of its maximum value in a d.C circuit containing inductance $\left(L\right)$ and resistance $\left(R\right)$ depends on

• A. $L$ only
• B. $R$ only
• C. $\frac{L}{R}$ only
• D. $LR$ only

Answer 1

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

Applying above given concept, $i=i_0(1-e^{\frac{-t}{\tau }})$
where, $\tau =$ time constant $=\frac{L}{R}$, $L=$ inductance, $R=$ resistance
According to question, $0.63i_0$ = $i_0(1-e^{\frac{-t}{\tau }})$
$e^{\frac{-t}{\tau }}=0.37$
Taking natural log ln both side:
$t=-\tau ln\left(0.37\right)$

Time, $t$ depends on time constant $\left(\tau \right)$ or $\frac{L}{R}$.