Question

A choke coil has an inductance of $4H$ and a resistance of $2\Omega$ . It is connected to a battery of $12V$ and negligible internal resistance. The time taken for the current to become $3.78A$ is nearly_____

• A. $8s$
• B. $3s$
• C. $2s$
• D. $4s$

Answer 1

Answer: (C)

$2s$

$L=4H,R=2\Omega$
$I_o=\frac{12}{2}$
$=6A$

At time t, $i=3.78A$
$3.78=I_o(1-e^{-t\frac{R}{L}})$
$3.78=6(1-e^{-t\times \frac{2}{4}})$
$\exp \left(\frac{-t}{2}\right)=0.37$
$t=1.988$
$\approx 2sec$

Method 2
Also, we observe that $\frac{3.78}{6}=.63$
i.e. $3.78A$ is $63\%$ of $I_o$ Therefore, it will take nearly one time constant for reaching $I=3.78A$
$T=\frac{L}{R}=\frac{4}{2}=2secs$