Solve for all voltages and currents List all responses in ph

Solve for all voltages and currents. List all responses in phasor form . Also, solve for the rms power of each component, and the power factor of the output

Solution

Ans) Given Source voltage peak Vp=15 V, RMS Value Vs=Vp/sqrt(2)=15/1.414=10.61 V

in phasor form Vs=10.61<0^o V (RMS Values)

Frequency F=1 kHz ,Angular Frequency w=2*pi*F=6283.185 rad/sec

Reactance of Capacitor C1= Xc1=1/(wC1)=497.36 ohms

Reactance of inductor L1=Xl1=wL1=0.063 ohms

R1=2000 ohms Given

Current I=Vs/(R1+jXl1-jXc1)=10.61<0^o/(2000+j0.063-j497.36)

I=5.15<13.96^o mA

Vout=I*R1=10.296<13.96^o V

Vc1=I*-jXc1=2.56<-76.04^o V Voltage across capacitor c1

Vl1=I*jXl1=3.244*10^-4<103.96^o V Voltage across inductor l1

Current I is same through all the elements as they are in series

RMS Power across R1=|I|²*R1=|5.15*10^-3|²*2000=0.053 W

C1=|I|²*Xc1=|5.15*10^-3|²*497.36=-j0.013 VAR because capacitor (Reactive Power as Real power is zero)

L1=|I|²*Xl1=|5.15*10^-3|²*0.063=j1.67 micro VAR because inductor (Reactive Power as Real power is zero)

Power factor of output Resistance is 1 unity as it is resistive load whereas for circuit or source power factor is

cos13.96=0.97 leading Source side power factor

cos0=1 for load side resistive load