For the circuit shown, (a) Determine the frequency of the voltage source (b) Det
ID: 1637322 • Letter: F
Question
For the circuit shown, (a) Determine the frequency of the voltage source (b) Determine X_L, and the X_c (c) Determine the impedance of the circuit (d) Determine the resonance frequency of the circuit (e) Determine the RMS voltage across the resistor, V_R rms (f) Determine the RMS voltage across the inductor, V_L rms (g) Determine the RMS voltage across the capacitor, V_C rms. (h) Determine the RMS voltage across the Source, V_S rms (i) Draw the phase diagram for the voltage across the inductor, the capacitor and the resistor and the voltage across the source. (j) Energy consumed by the resistor over one cycle. (k) Show that energy consumed by the inductor over one cycle is zero. (1) Show that energy consumed by the capacitor over one cycle is zero. (m) Determine the voltage across the inductor at resonance. (n) Determine the voltage across the capacitor at resonance. (o) Determine the voltage across the resistor at resonance.1LQ -% 1HExplanation / Answer
Q1.
part a:
angular frequency of voltage source=500 rad/sec
hence frequency=angular frequency/(2*pi)
=500/(2*pi)
=79.577 Hz
part b:
Xl=angular frequency*L
=500*1=500 ohms
part c:
Xc=1/(angular frequency*C)
=1/(500*10^(-6))=2000 ohms
part d:
resonance frequency=1/(2*pi*sqrt(L*C))
=1/(2*pi*sqrt(1*10^(-6)))
=159.15 Hz
part e:
in phasor form with maximum values,
voltage=140<0 volts
total impedance=1000+j(500-2000)=1000-j1500 ohms
current=140/(1000-j1500)
=0.043077+j0.064615 A
voltage across resistance=1000*current
=43.077+j64.615 volts
maximum voltage magnitude=sqrt(43.077^2+64.615^2)
=77.658 volts
Vrms=77.658/sqrt(2)
=54.912 volts
part f:
voltage across inductor=j500*current
=-32.308+21.538 j volts
rms value=sqrt(32.308^2+21.538^2)/sqrt(2)
=27.456 volts
part g:
voltage across capacitor=-j2000*current
=129.231 - j86.154 volts
rms value=sqrt(129.231^2+86.154^2)/sqrt(2)
=109.83 volts
part h:
rms voltage across the source=140/sqrt(2)=98.995 volts