Electro Magnetic Induction And Alternating Currents Question 308
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 [MP PMT 1994]
Options:
A) $ \frac{{{e}^{1/2}}}{{{e}^{1/2}}-1} $
B) $ \frac{e^{2}}{e^{2}-1} $
C) $ 1-{{e}^{-1}} $
D) $ {{e}^{-1}} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ 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{5}{10}=1.5 $
$ i_{1}=1.5(1-{{e}^{-R/L}})=1.5(1-{{e}^{-2}}) $
Þ $ \frac{{i_{\infty }}}{i_{1}}=\frac{1}{1-{{e}^{-2}}}=\frac{e^{2}}{e^{2}-1} $
