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Exam 2 - Circuit Branch Analysis

This exam is an individual student take home test. Absolutely no help from any person will be allowed. The exam will review lecture concepts discussed such as; phasor diagrams, equivalent circuits, AC series and AC parallel circuits, passive components, resistance and inductance, magnitude and phase relationship, superposition, KVL, KCL, loop analysis, and node analysis. Students must show all work in a neat and logical order. Good luck.

1. An AC Signal Generator is connected in series with a resistor, inductor, and capacitor with the following values:

f = 1.5MHz, C = 1.5 micro farads, ZT = 1 angle 30deg

a) Draw a phasor diagram
b) Find the value of R
c) Find the value of L
d) At what frequency does the circuit have a total impedance, ZT = 1.0535 angle 34.716deg

2. Find the voltage across the capacitor in Figure 1 using the following methods (remember to show all your work):

a) Nodal Analysis
b) Loop Analysis
c) Superposition

3. Find the following parameters for the circuit in Figure 2. Note the three branches.

Branch 1:
a) Impedance for Branch 1, Z1-1
b) Current for Branch 1, I1
c) Power for Branch 1, P1
d) Find Q1
e) Find S1
f) Find COSθ1

Branch 2:
a) Impedance for Branch 2, Z2-2
b) Current for Branch 2, I2
c) Power for Branch 2, P2
d) Find Q2
e) Find S2
f) Find COSθ2

Branch 3:
a) Impedance for Branch 3, Z3-3
b) Current for Branch 3, I3
c) Power for Branch 3, P3
d) Find Q3
e) Find S3
f) Find COSθ3

Total Circuit:
a) Total Impedance, ZT
b) Total Current, IT
c) Total Power, PT
d) Find QT
e) Find ST
f) Find COSθT

4. For the parallel circuit in Figure 2, find an equivalent series circuit.

Solutions: Provided in the Exam Notes Calculations Section below.

Exam Calculations and Notes
Exam Notes Page 1 of 5
Exam Notes Page 2 of 5
Exam Notes Page 3 of 5
Exam Notes Page 4 of 5
Exam Notes Page 5 of 5

Engineering key words: AC circuits, series, parallel, loop analysis, superposition, phase diagram, resistor, inductor, capacitor, resistance, inductance, capacitance, RL, RC, RLC, passive, KVL, KCL, node analysis, networks, AC signal, equivalent circuit modeling, equation, power, voltage law, current law, wire, relationships.

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