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 $t=\frac{ln2}{8}$, the current in the branch of capacitor is $200$ times the current in the branch of inductor .
• C. At $t=\frac{1}{8}ln\left(\frac{5}{4}\right)$, the potential drop across inductor is $4$ time the potential drops across capacitor .
• D. The potential drop across inductor is maximum at $t=0$.

Answer 1

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

$I=I_o(1-e^{-Rt/2})$

$I_{max}\alpha I_o=\frac{V}{R_1}=\frac{50}{75}=2A$

In index $fo$ in capacitor

$\theta ={\theta }_o(1-c\frac{-Rt}{Rc})$

$\frac{d\theta }{dt}=i=\theta \frac{t}{Rc}(1-e^{-\frac{1}{Rc}t})$

$\frac{1}{2}ma=\frac{{\theta }_o}{Rc}=\frac{CV}{RC}=\frac{50}{5000}=\frac{1}{100}$

Ratio is 200 .