Question

The inductance of a solenoid is $5\text{H}$ and its resistance is $5\Omega$. If it is connected to a $10\text{Volt}$ battery, then time taken by the current to reach ${\frac{9}{10}}^{th}$ of its maximum will be

• A. $4.0\text{s}$
• B. $2.3\text{s}$
• C. $1.4\text{s}$
• D. $1.2\text{s}$

Answer 1

The correct option is B $2.3\text{s}$

For inductance with internal resistance,
$I=I_0(1-e^{-\frac{R}{L}t})$
Given, $I=\frac{9I_0}{10}$
$\frac{9I_0}{10}=I_0(1-e^{-\frac{5}{5}t})\Rightarrow e^{-t}=\frac{1}{10}$
After taking log on both sides
$t=lo{g}_{e}10=2.3\text{sec}$