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: C -256 ?F and C2-225 ?F. The inductance is L-248 mh. At time t-0, the current through the inductor- has its maximum value IL(0)-214 mA and it has the direction shown. . 1) What is oo, the resonant frequency of this circuit? radians/s 2) What is Qj(t1), the charge on the capacitor C, at time t t 20 ms? The sign of Q, is defined to be the sameas the sign of the potential difference Vab" Va-Vb at time t 3) What is Vb)V-Ve the voltage across the inductor at time t, -20 ms? Note that this voltage is a signed number. 4) W hat is Q1,max, the magnitude of the maximum charge on capacitor C,?

Explanation / Answer

since capacitors are connected in series

1/Ceq = 1/C1 + 1/C2

1/Ceq = 1/256+1/225

Ceq = 119.75 uF

w0 = 1/ sqrt LCeq = 1/sqrt (0.248) (119.75* 10^-6) = 183.499 rad/s

(b)

Q max = I max/ wo = 0.214/183.499 = 1.16 * 10^-3 C

Q( t1) = Q max sin w t1

= 1.16 * 10^-3 * sin ( 183.499*20* 10^-3 s)

= -5.84 * 10^-4 C

(c)

V( t1) = - Lwo I max sin ( wt)

= -0.248 ( 183.499) ( 0.214* sin ( 183.499 * 20* 10^-3)

= 4.90 V

(d)

Qmax = I max/ wo = 0.214/183.499 = 1.16 * 10^-3 C

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