At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating…

At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current It=I0cos⁡ωt , with I0=1A and ω=500  rad/s starts flowing in it with the initial direction shown in the figure. At t=7π6ω , the key is switched from B to D. Now onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C=20 μF, R=10 Ω and the battery is ideal with emf of 50V, identify the correct statement(s).

  1. Magnitude of the maximum charge on the capacitor before t=7π6ω is 1×10-3 C .
  2. The current in the left part of the circuit just before t=7π6ω is clockwise.
  3. Immediately after A is connected to D, the current in R is 10 A.
  4. Q=2×10-3 C .

Solution

Given,I=I0cosωt, Peak or maximum current I0=1A           angular frequency,ω=500 rad s-1           capacitance C=20μF           resistance R=10Ω          battery voltage V=50VIf q represent the charge on capacitor’s upper plate:
It=I0cos⁡(ωt) 
⇒qt=I0ωsin⁡ωt
∴ Max charge qmax=1A500Rads=2×10-3C
Charge of upper plate at t=76ω
=I0ωsin⁡7πω =-I02ω
When capacitor is fully charged then charge on upper plate =50v×20μf
=10×10-3C
⇒Q=1×10-3-I02ω=2×10-3C
Voltage across capacitor when A and D are connected =1×10-3C20×10-6μf=50V
Total voltage across R=100V
Current is anticlockwise

Asked in: JEE Advanced 2014 (Paper 1)

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