Question

# Two resistors, one inductor  and a capacitor are connected in a circuit with a battery and switch as shown in figure. The charges on capacitor and current in inductor is zero at $$t=0$$.Now switch is closed at $$t=0$$, then choose the correct options(s).

A
The ratio of maximum current in the branch of inductor to the branch of capacitor is 200.
B
At t=ln28, the current in the branch of capacitor is 200 times the current in the branch of inductor .
C
At t=18ln(54), the potential drop across inductor is 4 time the potential drops across capacitor .
D
The potential drop across inductor is maximum at t=0.

Solution

## The correct option is A The ratio of maximum current in the branch of inductor to the branch of capacitor is $$200$$.for $$Rt$$ circuit $$I=I_{o} (1- e^{-Rt/2})$$$$I_{max} \alpha I_{o}= \dfrac{V}{R_{1}}= \dfrac{50}{75}= 2A$$In index $$fo$$ in capacitor $$\theta = \theta_{o} (1- c \dfrac{-Rt}{Rc})$$$$\dfrac{d\theta}{dt}=i= \theta \dfrac{t}{Rc} (1-e^{-\dfrac{1}{Rc}t})$$$$\dfrac{1}{2}ma =\dfrac{\theta_{o}}{Rc}= \dfrac{CV}{RC}= \dfrac{50}{5000}=\dfrac{1}{100}$$Ratio is 200 . General Knowledge

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