ECE 461/661 Mid-Term
1. Phasor: Convert the following voltage and current signals into phasor (both rectangular and polar
forms) [20points]
a) 𝑣(𝑡) = 100 cos(𝜔𝑡 + 30𝑜 ) V
b) 𝑖(𝑡) = 5√2 cos(𝜔𝑡 − 45𝑜 ) V
c) 𝑣(𝑡) = 100 cos(𝜔𝑡 − 45𝑜 ) + 100 cos(𝜔𝑡) A
d) 𝑖(𝑡) = 5√2 cos(𝜔𝑡 + 45𝑜 ) + 5√2 cos(𝜔𝑡 + 15𝑜 ) A
2. Single Phase: [35 points] 𝑅𝐿 & 𝐶𝐿 together are the load in the circuit shown below. The voltmeter
measures 180 V, the ammeter measures 10 A, and the wattmeter measures 1440 W. Find the following:
a) The value of the load resistor 𝑅𝐿
b) The value of the capacitor 𝐶𝐿
c) The apparent power |S|
d) The complex power S
e) The power factor pf
f) The power factor is: leading or lagging?
g) The two components of the load are in
a box which cannot be opened. Add
(draw it) another component to the circuit above which can correct the power factor (make pf =
1). Show the correct component in the correct place and find its value. This component should
not affect the real power consumption of the load.
Hint: Similar to Ex3 of the Single-Phase AC power examples.
3. Three Phase: What is the Y/Δ transformation [5 points]
4. Three Phase: here we have a Δ load connected to a
three phase sources via transmission lines (RL =1 Ω)
[10 points]
a) What does the ammeter measure? Line
current or load current.
b) Transform the circuit into the equivalent Y
circuit. Draw the equivalent circuit.
c) Find the total power consumption in this
circuit (P and Q)
d) What is the power consumption of the load (P
and Q)? Hint: subtract the total power
consumption in question c to the power loss
due to line resistance
e) What is the line voltage at the load (Only RMS)?
5. Three Phase: Which one is constant? The instantaneous single phase AC power or the instantaneous
three phase AC power? [10 points]
6. Transformer: [20 points]
a) Please name four assumptions used in the model of the ideal transformer
b) Please draw the equivalent circuit of practical transformer model.
c) Which parameters of the transformer are determined by short circuit test?
d) Which parameters of the transformer are determined by open circuit test?