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Question

A circuit is shown below.


Currently the switch is in position A and steady current is flowing through circuit. Capacitor is uncharged. At t=0, switch is instantly moved to position B.
Find the current in the LC circuit.(Given that ω = 1LC)

A
VRsin(ωt)
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B
VRcos(ωt)
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C
VRcos(ωt+π5)
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D
VRcos(ωt+π8)
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Solution

The correct option is B VRcos(ωt)
At t=0, there is a steady current downward through the inductor i.e.
i(0)=VR
For t0, krichhoff's law gave following for the LC circuit
Ld2Idt2=qC .....(i)
Here q is the charge on the lower plate of the capacitor and we know
I= dqdt
so differentially equation (i), we get
d2Idt2=ILC=ω2I ...(ii)
The general solution (ii) is given by
I= Imaxcos(ωt+ϕ)
Using initial condition of current i=VR, we get ϕ=0
So,
I= VRcos(ωt)

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