AC Circuit Analysis Second Midterm Prof. Diego Mejía November 13, 2020 Name: ID: Use class notes and textbooks if really needed. Computer and inter...

AC Circuit Analysis
Second Midterm
Prof. Diego Mejía
November 13, 2020
Name: ID:
Use class notes and textbooks if really needed. Computer and internet is also allowed. Communication with other people is prohibited, 110-minute time limit. Good luck!!.
Problem 1. Let the circuit shown in Fig. 1 in which Vs = 100 0◦ V and ZL = 32 + j20 Ω.
+
−Vs
j2 Ω
a 2 Ω
j4 Ω
b
j8 Ω
1 Ω c
ZL
+
−
V0
d
−j16 Ω
j2 Ω
Figure 1: Linear transformer of problem 1
(a) (8 points.) Compute the T-equivalent circuit of the linear transformer.
(b) (16 points.) Find V0.
Problem 2. Consider your electrical circuit at home. An oven and a refrigerator are connected in parallel to the secondary winding of a transformer placed nearby. And the primary winding connects the generation system through a line with impedance 1 + j15Ω. Assume the oven can be represented by a 20 Ω resistor, the iron by a 15 Ω resistor, and the refrigerator by an admittance 1/60 − j/60 S.
(a) (20 points.) If the current through the oven, seen from the source side, is 0.59748−j0.01180 A, what is the current flowing through the secondary winding Is?
(b) (24 points.) If the voltage at the terminals of your generator is Vg = 1200 0◦ V, what should be the turns ratio (a) of the transformer? [Note: keep in mind that a is a real number.]
1
+
−
Vp
−
+
Vs
Is
Oven
I1
Iron
I2
Refrigerator
I3
a : 1
Figure 2: Circuit of problem 2
a b
jX1
+ −V1
Ix
jX2
− +V2
jX3
+ −V3
Iy
jX13 jX23
Figure 3: Circuit of problem 3
Problem 3. Consider the circuit in Fig. 3:
(a) (12 points.) Complete the following 3 × 2 impedance matrix that represents voltages in terms of currents in the magnetically coupled inductance array: V1V2
V3
 = j
 
3×2
(
Ix
Iy
)
(b) (20 points.) Determine the equivalent inductor seen between terminals a and b.
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