Consider an AC circuit problem with a 100 Vrms 60 Hz source connected to a resis
ID: 2136814 • Letter: C
Question
Consider an AC circuit problem with a 100 Vrms 60 Hz source connected to a resistor of R = 100 ohms, a capacitor of C = 10 microF, and an inductor of L = 1H, all in series.
1) Calculate the total impedance Z for the circuit in exponential form showings its magnitude and phase angle. Is the circuit resistive, capacitive, or inductive? Explain how you know the answer to the last question?
2)Calculate the magnitude of the rms value of the current, I in the circuit(what you would read on an AC ammeter).
3)What is the phase angle between I and the source of V? Does I lag or lead V? Explain?
4)Calculate the magnitude of the rms voltages across R,C, and L as measured by a voltmeter. Do they add up to the rms Voltage of the source? Should they? Explain. Does this have any ramifications for picking a voltage rating for C in the circuit? What should it be in this case?
5)Calculate the phase angle between Vc and V of the source. Does Vc lag or lead V?
6)Calculate the total power being expended by the source in this circuit.
7)At what frequency will the circuit be purely resistive? what is this frequency called? Is the current a max or min at this frequency? What is the phase angle between I and V of the source at this frequency?
Explanation / Answer
a) Z = impedance =R + J*L*W -J/(w*C) =100 + j*376.8 -J*265.4
= 100 + j*111.4
r = [100^2+111.4^2]^0.5 =149.69
theta =tan^-1[111.4/100] =48
hence Z =r<theta = 149.69<48
b)