An inductor and two identical capacitor are connected in the circuit as shown in the figure. Initially capacitor A has no charge and capacitor B has CV charge. Assume circuit has no resistance at all. At t = 0 switch S is closed, then [given $L C = \frac{2}{π^{2} \times 10^{4}} \sec^{2} & C V = 100 m C]$

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$q = 50 (1 - \cos 100 π t) m C$ , where q is the charge on capacitor B at time t.

When current in the circuit is maximum, charge on each capacitor is same

When current in the circuit is maximum charge on capacitor A is twice the charge on capacitor B

$q = 50 (1 + \cos 100 π t) m C$ , where q is the charge on capacitor B at time t

answer is A, C.

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Detailed Solution

$i \to \max$
$L \frac{d i}{d t} = 0$
$∴ v \to$ same for cap charge same
$\begin{array}{l} \frac{c v - q_{1}}{c} - \frac{q_{1}}{c} - l \frac{d i}{d t} = 0 \\ q_{1} - \frac{c v}{2} = A \sin (w t + θ) \end{array}$
$\begin{array}{l} I = A ω \cos (ω t + θ) \\ t = 0, i = 0 \Rightarrow θ = \frac{π}{2} \\ ∴ q_{_{1}} = \frac{c v}{2} - \frac{c v}{2} \cos ω t \Rightarrow q_{_{2}} = c v - q_{_{1}} \end{array}$