An inductor and two capacitors are connected in the circuit as shown in figure. Initially capacitor A has no charge and capacitor B has CV charge. Assume that the circuit has no resistance at all. at at=0, switch S is closed, then [given LC=2π2×104s2 and CV=100mC ]choose the correct option
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a
When current in the circuit is maximum, charge on capacitor A is thrice the charge on capacitor B
b
When current in the circuit is maximum, charge on capacitor A is twice the charge on capacitor B
c
q=50(1+cos100πt)mC , where q is the charge on capacitor B at time t
d
q=50(1−cos100πt)mC , where q is the charge on capacitor B at time t
answer is C.
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Detailed Solution
Ld2qdt2+qC−CV−qC=0 BY applying kirchoffs lawd2qdt2+2q−CVLC=0ω=2LC=22π2×104=100πq=CV2[1−cosωt]q'=CV−q=CV2[1+cosωt]=1002[1+cos100πt]=50[1+cos100πt]I=+CVω2sinωt