Two identical capacitors, each with a capacitance C, connected in series to a 12

Question

Two identical capacitors, each with a capacitance C, connected in series to a 12 V, 110-Hz ac generator draw a current of 0.015 A. The capacitance C of each capacitor is closest to: (a) 1.1 mu F (b) 1.7 mu F (c) 2.3 mu F (d) 2.9 mu F (e) 3.6 mu F A 40-mu F capacitor is connected in parallel with a 0.057 H inductor coil and to an ac generator. If the rms current through the capacitor is four times the rms current through the inductor (I_c = 4 I_L), the frequency of the generator is closest to: (a) 210 Hz (b) 240 Hz (c) 270 Hz (d) 300 Hz (e) 330 Hz An 85-Ohm resistor, a 2.0-mu F capacitor and a 50-mH Inductor are connected In series to a 35 V, 710-Hz ac generator. The rms current drawn from the ac generator is closest to: (a) 0.16 A (b) 0.20 A (c) 0.25 A (d) 0.30 A (e) 0.35 A

Explanation / Answer

Here,

11)

let the capacitance is C

V/I = 2/(2pi * f * C)

12/.015 = 2/(2pi * 110 * C

C = 3.62 *10^-6 F = 3.62 uC

e) 3.6 uF

12)

let the frequency is f

Now, as

I = V/Z

Ic = 4 * IL

(2pi * f * 40 *10^-6) = 4 * 1/(2pi * f * 0.057)

solving for f

f = 210 Hz

a) 210 Hz

13)

rms current = 0.707 * 35/(sqrt(85^2 + (1/(2 * pi * 710 * 2 *10^-6) - (2pi * 710 * 0.050))^2))

rms current = 0.16 A

the rms current is 0.16 A

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