

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, Z_{T} = 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, Z_{T} = 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, Z_{11}
b) Current for Branch 1, I_{1}
c) Power for Branch 1, P_{1}
d) Find Q_{1}
e) Find S_{1}
f) Find COS_{θ1}
Branch 2:
a) Impedance for Branch 2, Z_{22}
b) Current for Branch 2, I_{2}
c) Power for Branch 2, P_{2}
d) Find Q_{2}
e) Find S_{2}
f) Find COS_{θ2}
Branch 3:
a) Impedance for Branch 3, Z_{33}
b) Current for Branch 3, I_{3}
c) Power for Branch 3, P_{3}
d) Find Q_{3}
e) Find S_{3}
f) Find COS_{θ3}
Total Circuit:
a) Total Impedance, Z_{T}
b) Total Current, I_{T}
c) Total Power, P_{T}
d) Find Q_{T}
e) Find S_{T}
f) Find COS_{θT}


4. For the parallel circuit in Figure 2, find an equivalent series circuit.
Solutions: Provided in the Exam Notes Calculations Section below.
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.
