Suppose we connect a little 90mH solenoid with I=.165 amps in series with the 22

Question

Suppose we connect a little 90mH solenoid with I=.165 amps in series with the 220?F capacitor, powered by a 12V (peak) generator at 20Hz. . . . a) compute the Resistive, Capacitative, and Inductive Reactances of the series devices, individually. . . . b) compute the total Impedance of all series devices, and the current thru them ; does the current lead, or lag, the voltage? . . . c) repeat (a) and (b) for a 60Hz frequency . . . d) repeat for their resonance frequency ... why is the current not infinite, at this resonance frequency?

Explanation / Answer

a) XL = 2 x pi x f x L = 2 x pi x 20 x 90 x 10-3 = 11.31 ohm

Xc = 1 / 2 x pi x f x C = 1/ 2 x pi x 20 x 220 x 10-6 = 36.17 Ohm

R = 0

b)

impedance

Z=sqrt[(Xl-Xc)^2]=sqrt[(11.31-36.17)^2]

Z=24.86 ohms

Maximum current

Ip=V/Z=12/24.86

Ip=0.4827 A

c)

at f=60 Hz

XL=2pi*60*90*10^-3=33.93 ohms

Xc=1/2pi*60*220*10^-6= 12.06 ohms

Z=sqrt[33.93-12.06)^2]=21.87

Ip=12/21.87=0.5487 A

d)

resonant frequency

f=1/2pisqrt(LC) =1/2pi*sqrt(90*10^-3*220*10^-6)

f=35.77 Hz

XL=2pi*35.77*90*10^-3=20.23 ohms

Xc=1/2pi*35.77*220*10^-6=20.23 ohms

since XL=Xc

Z=sqrt[(20.23-20.23)^2]=0 ohms

so

Ip=V/Z =12/0 =infinity

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