Question

An emf of $15$ $V$ is applied in a circuit containing $5$ $H$ inductance and $10\Omega$ resistance. The ratio of the currents at time $t=\infty$ and $t=1$ $s$ is:

• A. $\frac{e^{0.5}}{e^{0.5}-1}$
• B. $\frac{e^2}{e^2-1}$
• C. $1-e^{-1}$
• D. $e^{-1}$

Answer 1

Answer: (B)

$\frac{e^2}{e^2-1}$

$i=\frac{E}{R}(1-e^{\frac{-Rt}{L}})$

$I_{t=\infty }=I_0$ (where, $I_o=\frac{E}{R}$)

$I_{t=1s}=I_0(1-e^{-\frac{10}{5}\times 1})$

$=I_0(1-e^{-2})=I_0(1-\frac{1}{e^2})$

$\therefore =\frac{I_{t=\infty }}{I_{t=1s}}=\frac{I_0{e}^2}{I_0(e^2-1)}=\frac{e^2}{e^2-1}$