When the capacitor gets charged completely, is opened and is closed. Then, [2006]

Question

In the given circuit the capacitor (C) may be charged through resistance R by a battery V by closing switch $S_{1}$ . Also when $S_{1}$ is opened and $S_{2}$ is closed the capacitor is connected in series with inductor (L).

Q. When the capacitor gets charged completely, $S_{1}$ is opened and $S_{2}$ is closed. Then, [2006]

Smart Achievers · Accepted Answer

(4)

Instantaneous charge on plates at any time $t$ during discharging

$Q_{inst} = Q_{0} \cos ω t$

$∴$ Instantaneous current,

$I_{inst} = \frac{d Q}{d t} = Q_{0} ω \sin ω t$

$∴$ $I_{\max} = Q_{0} ω$

Here, $Q_{0} = C V$ and $ω = \frac{1}{\sqrt{L C}}$

$∴$ $I_{\max} = C V \times \frac{1}{\sqrt{L C}} = V \sqrt{\frac{C}{L}}$

Solution

1 at $t = 0$ , energy stored in the circuit is purely in the form of magnetic energy

2 at any time $t > 0$ , current in the circuit is in the same direction

3 at $t > 0$ , there is no exchange of energy between the inductor and capacitor

4 at any time $t > 0$ , instantaneous current in the circuit may be $V \sqrt{\frac{C}{L}}$

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Solution

1 at t=0, energy stored in the circuit is purely in the form of magnetic energy

2 at any time t>0, current in the circuit is in the same direction

3 at t>0, there is no exchange of energy between the inductor and capacitor

4 at any time t>0, instantaneous current in the circuit may be VCL

Ans. (4) Instantaneous charge on plates at any time t during discharging Qinst=Q0cosωt ∴ Instantaneous current, Iinst=dQdt=Q0ωsinωt ∴ Imax=Q0ω Here, Q0=CV and ω=1LC ∴ Imax=CV×1LC=VCL

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1 at $t = 0$ , energy stored in the circuit is purely in the form of magnetic energy

2 at any time $t > 0$ , current in the circuit is in the same direction

3 at $t > 0$ , there is no exchange of energy between the inductor and capacitor

4 at any time $t > 0$ , instantaneous current in the circuit may be $V \sqrt{\frac{C}{L}}$