Question

An ideal coil of $10 \text{ H}$ is connected in series with a resistance of $5 \, \Omega $ and a battery of $5 \text{ V}$ . $2$ seconds after the connection is made, the current flowing in ampere in the circuit is

• A. $\left(1-e^{-1}\right)$
• B. $\left(1 - \textit{e}\right)$
• C. $\textit{e}$
• D. $\textit{e}^{-1}$

Answer 1

Answer: (A)

During the growth of current in $L R$ circuit is given by
$I=I_0\left(1-e^{-\frac{R}{L} t}\right)$
or $I=\frac{E}{R}\left(1-e^{-\frac{R}{L} t}\right)=\frac{5}{5}\left(1-e^{-\frac{5}{10} \times 2}\right)$
$I=\left(1-e^{-1}\right)$