Question

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

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

Answer 1

Answer: (D)

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

Time constant of LR circuit is given by:

$\tau =\frac{L}{R}$

$=\frac{5}{10}=0.5s$

Current at time $t$ is given by:

$i\left(t\right)=i_{\infty }(1-e^{-t/\tau })$

$⟹\frac{i\left(\infty \right)}{i\left(1\right)}=\frac{i_{\infty }}{i_{\infty }(1-e^{-1/0.5})}$

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