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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).
1902758_1205d104a3ef4d559cacff5f931205ea.png


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

1893369_1902758_ans_cab397a40eca44c59ce40f1c282c4cf7.png

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