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 = 473 F and C2 = 328 F. The inductance is L = 370 mH. At time t =0, the current through the inductor has its maximum value IL(0) = 258 mA and it has the direction shown.

1)

What is o, the resonant frequency of this circuit?

radians/s

2)

What is Q1(t1), the charge on the capacitor C1 at time t = t1 = 31 ms? The sign of Q1 is defined to be the sameas the sign of the potential difference Vab = Va - Vb at time t = t1.

C

3)

What is Vbc(t1)= Vb - Vc, the voltage across the inductor at time t1 = 31 ms? Note that this voltage is a signed number.

V

4)

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

C

Explanation / Answer

Since figure is not given in the ques so I consider capacitor to be connected in parallel.

Ceq=C1+C2=437+328=765microF

A)w=1/L*Ceq=1/370*10^-3*765*10^-6=59.44rad/s

B)Q=I*t1=258*10^-3*31*10^-3=7.998*10^-3 C

C)V=Q/C=7.998*10^-3/765*10^-6=10.455V

D)V=I*XL=I*w*L=258*10^-3*59.44*370*10^-3=5.674V

Q=C*V=437.10^-6*5.674=2.4796*10^-3C

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