Question

An e.m.f. of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time $t=\infty$ and at t =1 second is

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

Answer 1

The correct option is B $\frac{e^2}{e^2-1}$


$i=i_0(1-e^{-Rt/L})$
$i_0=\frac{E}{R}$ (Steady current) When $t=\infty$
$i_{\infty }=\frac{E}{R}(1-e^{-\infty })=\frac{15}{10}=1.5$
$i_1=1.5(1-e^{-R/L})=1.5(1-e^{-2})\Rightarrow \frac{i_{\infty }}{i_1}=\frac{1}{1-e^{-2}}=\frac{e^2}{e^2-1}$