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Exam 1 - Circuit Impedance Analysis

The following exam is in two parts. The first part is multiple choice. The student should read the question, decide on the correct answer and circle the correct letter. The second part of the exam is problem solving. There are two problems with multiple answers. All numeric answers should be enclosed in a box. All work should be in a neat and logical form for maximum credit. The exam will review lecture concepts relating to; thevenin equivalent circuit, max power transfer, loads, total impedance, coils, voltage sources and current sources, magnitude and phase angle, complex notation, rectangular and polar, susceptance, admittance, and power factor. Good luck.

1. For the circuit in Figure 1. If R = 50Ω and XL = 20Ω, Find ZT and θT
a. 53.85Ω angle -68.2deg
b. 53.85Ω angle +68.2deg
c. 53.85Ω angle -21.8deg
d. 53.85Ω angle +21.8deg

2. For the circuit in Figure 2. What is the total impedance ZT in Polar form?
a. 10Ω angle 5deg
b. 5Ω angle 10deg
c. 11.18Ω angle 26.6deg
d. 11.18Ω angle 63.43deg

3. What is the susceptance of a 100μF capacitor at 1000Hz?
a. 0.63S
b. 1.59S
c. 104S
d. 10-4S

4. For the series circuit in Figure 3. Determine the total impedance ZT expressed in Rectangular form.
a. 64.3Ω + j76.6Ω
b. 86.6Ω + j50Ω
c. 100Ω + j30Ω
d. 100Ω + j50Ω

5. A circuit has a power factor of 0.8 lagging. The circuit dissipates 100W of power with an input voltage of 500V. What is the impedance of the circuit expressed in Rectangular form?
a. 1200Ω - j1600Ω
b. 1200Ω + j1600Ω
c. 1600Ω - j1200Ω
d. 1600Ω + j1200Ω

6. For the circuit configuration in Figure 4. What is the total impedance ZT for this circuit?
a. 10Ω - j12Ω
b. 10Ω + j12Ω
c. 10Ω - j2Ω
d. 10Ω - j2.4Ω

7. Given the circuit in Figure 4. If IS = 1A ∠ 80deg, what is the current through the coil?
a. 0.5A angle -100deg
b. 0.5A angle +100deg
c. 2A angle -100deg
d. 2A angle +100deg

8. For the circuit in Figure 5. As the frequency increases, the total impedance ZT of the circuit?
a. becomes more resistive
b. becomes more inductive
c. becomes more capacitive
d. increases, approaches infinity

9. Given the circuit in Figure 6, what is the total admittance YT for this circuit?
a. 63.73S angle 11.31deg
b. 0.016S angle -11.31deg
c. 0.028S angle -56.31deg
d. 0.02S angle 90deg

10. For the circuit in Figure 6, what is the value of the current in I1
a. 1.39A angle -26.31deg
b. 0.72A angle 26.31deg
c. 1A angle -120deg
d. 1A angle 120deg

11. Given the circuit in Figure 7, calculate the following parameters:
a. The total impedance ZT
b. The voltage across the current source Vt
c. The voltage across the coil, V1

12. Given the circuit in Figure 8, calculate the following:
a. Find a thevenin equivalent circuit. Find Vth and Zth and draw the equivalent circuit.
b. What value should the impedance load Zload be to ensure maximum power transfer?
c. What is the maximum power that could be delivered to the load, Pmax?

Solutions: Provided in the Exam Notes Calculations Section below.

Exam Calculations and Notes
Exam Notes Page 1 of 4
Exam Notes Page 2 of 4
Exam Notes Page 3 of 4
Exam Notes Page 4 of 4

Engineering key words: Circuit test, examination, solutions, answers, AC, alternating current, Thevenin, Norton, equivalent circuit, polar, resistance, inductance, capacitance, RL, RC, RLC, passive component, total impedance, cap, delta, calculation, admittance and susceptance, phase and complex notation, power, watts, voltage, current, peek to peek, frequency, load, max and min.

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