UNIVERSITY OF MASSACHUSETTS DARTMOUTH
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ECE 201 CIRCUIT THEORY 1
TAKE – HOME PROBLEMS
PROBLEM #1 (10%)
Find the rms value of the half-wave rectified sinusoidal voltage shown below.
PROBLEM #2 (20%)
An 80 kHz sinusoidal voltage has zero phase angle and a maximum amplitude of 25 mV. When
this voltage is applied across the terminals of a capacitor, the resulting steady – state current
has a maximum amplitude of 628.32 µA.
a)
b)
c)
d)
e)
What is the frequency of the current in radians per second?
What is the phase angle of the current?
What is the capacitive reactance of the capacitor?
What is the capacitance of the capacitor in microfarads?
What is the impedance of the capacitor?
PROBLEM #3 (20%)
a) For the circuit shown below, find the frequency (in radians per second) at which the
impedance Zab is purely resistive.
b) Find the value of Zab at the frequency determined in part a.
PROBLEM #4 (20%)
Use the concept of voltage division to find the steady – state expression for vo(t) if the applied
voltage is vg(t) = 75cos20,000t V.
PROBLEM #5 (15%)
Use the node – voltage method to find voltage Vo in the circuit shown below.
PROBLEM #6 (15%)
The circuit is operating in sinusoidal steady – state.
Find the value of ω if
io=40sin(ωt + 21.87°) mA
vg=40cos(ωt - 15°) V.