EE233
Homework 2
Due: 0900 Tuesday 23 September, 2014
Problem 1
a. Show that at a given frequency
ω
, the circuits in Fig. 1(a) and (b) will have the same
impedance between the terminals a, b if
R
2
=1+ω
2
R
1
2
C
1
2
ω
2
R
1
C
1
2
C
2
=C
1
1+ω
2
R
1
2
C
1
2
b. Find the values of resistance and capacitance that when connected in parallel will give the
same impedance at 50 krad/s as that of a 1kΩ resistor connected in series with a
capacitance of 40nF.
Figure 1
Problem 2
At t = -250/6 µs, a sinusoidal voltage v(t) is known to be zero and going positive. The voltage is
next zero at t = 1250/6 µs. It is also know that the voltage is 75V at t = 0.
a. What is the frequency of v(t) in hertz ?
b. What is the expression for v(t) ?
Problem 3
For the circuit in Fig. 3, suppose
va=20 cos
(
2000 t−36.87 °
)
V
vb=10 cos
(
5000 t+16.26 °
)
V
a. Find the steady-state expression for
v0(t)
?
