Question

An ideal coil of $10H$ is connected in series with a resistance of $5\Omega$ and a battery of $5V.$ $2$ second after the connection is made the current following in amperes in the circuit is:

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

Answer 1

The correct option is D $\left(1{-e}^{-1}\right)$

Given that,

$R=5\Omega$

$L=10H$

$t=2seconds$

$V=5V$

The current equation is given by,

$I=I_0[1-e^{\frac{-Rt}{L}}]$

$I_0=\frac{V}{R}=\frac{5}{5}=1A$

$I=1[1-e^{\frac{-10}{10}}]$

$=(1-e^{-1})$