A circuit is constructed with two capacitors and an inductor as shown. The value

Question

A circuit is constructed with two capacitors and an inductor as shown. The values for the capacitors are: C1= 421 ?F and C2 = 222 ?F. The inductance is L = 245 mH. At time t =0, the current through the inductor has its maximum value IL(0) = 128 mA and it has the direction shown.

I got this one:

1) What is ?o, the resonant frequency of this circuit? Answer: 167.573 radians/s

but I still can't get these ones:

2) What is Q1(t1), the charge on the capacitor C1 at time t = t1 = 21.9 ms? The sign of Q1 is defined to be the sameas the sign of the potential difference Vab = Va - Vb at time t = t1.

3) What is Vbc(t1)= Vb - Vc, the voltage across the inductor at time t1 = 21.9 ms? Note that this voltage is a signed number.

4) What is Q1,max, the magnitude of the maximum charge on capacitor C1?

Explanation / Answer

2)since at t=0 i is max so i(t)=0.128*cos(wt) where w is the frequency

so integrate it ot find charge

q=0.128/w*sinwt=7.638*10^-4*sin(wt) C

at t=t1=21.9ms

q=7.638*10^-4*sin(167.573*21.9*10^-3)=-3.85*10^-4 C

3)Vab=Q/C1=-3.85*10^-4/(421*10^-6)=-0.9144V

4)C1 max=C2max=7.638*10^-4 when sin(wt)=1

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