Question

A e.m.f. of 15 volt is applied in a circuit of inductance 5 henry and resistance 10 $\omega$. The ratio of currents flowing at $t=\infty$ and $t=1$ second will be:

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

Answer 1

Answer: (B)

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

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

$i(t=1)=\frac{E}{R}(1-e^{-R/L})=\frac{E}{R}(1-e^{-2})$

$\frac{i(t=\infty )}{i(t=1)}=\frac{\frac{E}{R}(1-e^{-2})}{\frac{E}{R}}=\frac{e^2-1}{e^2}$