Question

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

• A. $4.0s$
• B. $2.3s$
• C. $1.4s$
• D. $1.2s$

Answer 1

The correct option is B $2.3s$

Given,

Inductance $L=5H$

Resistance $R=5\Omega$

Current relation $i=i_o(1-e^{-t\frac{R}{L}})$

Time required to reach ${\left(\frac{9}{10}\right)}^{th}$ of maximum current.

$\frac{9}{10}{i}_o=i_o(1-e^{-t\frac{R}{L}})$

$\frac{9}{10}{i}_o=i_o(1-e^{-t\frac{5}{L}})\Rightarrow e^{-t}=\frac{1}{10}$

$t=2.3\sec$