resistance R=2.5 ohms
inductance L=100*10^-6 H
capacitance C=87.5*10^-6 F
a)
Vrms=5.6 v
f=120 Hz
===> w=2pif=2pi*120 = 753.98 rad/sec
Imax=Vmax/sqrt(R^2+(wL-1/wC)^2)
Imax=Vrms*sqrt(2)/sqrt(R^2+(wL-1/wC)^2)
Irms=Imax/sqrt(2) =vrms/(sqrt(R^2+(wL-1/wC)^2))
Irms=5.6/(sqrt(2.5^2+(753.98*100*10^-6-1/(753.98*87.5*10^-6))^2)
Irms=0.36 A
b)
tan(theta)=(WL-1/WC)/R
tan(theta)=(753.98*100*10^-6-1/(753.98*87.5*10^-6))/2.5
theta=80.6 degrees
c)
f=5 kHz =5*10^3 Hz
===> w=2pif=2pi*5*10^3 = 31.41*10^3 rad/sec
Irms=Imax/sqrt(2) =vrms/(sqrt(R^2+(wL-1/wC)^2))
Irms=5.6/(sqrt(2.5^2+(31.41*10^3*100*10^-6-1/(31.41*10^3*87.5*10^-6))^2)
Irms=1.5 A
d)
tan(theta)=(WL-1/WC)/R
tan(theta)=(31.41*10^3*100*10^-6-1/(31.41*10^3*87.5*10^-6))/2.5
theta=48 degrees
e)
resonace frequency f=1/2pi*sqrt(LC)
f=1/(2pi*sqrt(100*10^-6*87.5*10^-6))
f=1701.44 Hz
f)
at resonance,
Irms=Vrms/R
Irms=5.6/2.5
Irms=2.24 A
g)
tan(theta)=(WL-1/WC)/R
tan(theta)=0
===> theta=0 degrees
