Consider the circuit depicted in the attached figure. The voltage source s an AC

Question

Consider the circuit depicted in the attached figure. The voltage source s an AC source of frequency f =25 Hz Randomized Variables R_1= 101 ohm R_2 = 101 ohm, C_1 = 1.5 mu F C_2 = 1.5 mu F L= 0.11 H a) Given the above circuit, write an expression for the total impedance Z for the circuit as a complex number. You may assume the current is a completely real phasor. (b) Given the values for resistance, inductance, and capacitance above, what is the magnitude of the phasor for the impedance Z in ohm. (c) Given the values for resistance, inductance, and capacitance above, what is the phase angle of the phasor for the impedance Z in degrees. (d) If the voltage supplied is of the form V = A cos(omega t) where A = 6 V, determine the current I supplied in A at time = 0.6 s. I_t =

Explanation / Answer

part a:

inductive reactance=Xl=2*pi*f*L

capacitive impedance of C1=Xc1=1/(2*pi*f*C1)

capacitive impedance of C2=Xc2=1/(2*pi*f*C2)

total impedance=R1+R2+i*(Xl-Xc1-Xc2)

=R1+R2+i*(2*pi*f*L-(1/(2*pi*f*C1))-(1/(2*pi*f*C2))

part b:

using the values given.

total impedance=202 - 8470.98 i ohms

impedance magntiude=Z=sqrt(202^2+8470.98^2)
=8473.4 ohms

part c:
phase angle of the phasor=arctan(-8470.98/202)=-88.634 degrees

part d:

V=6*cos(w*t)

=6*cos(2*pi*25*t)

current=V/total impedance

=(6/8473.4)*cos(2*pi*25*t-(-88.634 degrees))

at t=0.6 seconds, current

=1.688*10^(-5) A

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