ELEC 101
Prof. Rich Kozick
Spring, 1998

Homework Assignment 10

Date Assigned: Monday, March 23, 1998
Date Due: Friday, March 27 and Monday, March 30, 1998

Reading: Relevant reading in the Bobrow text to supplement the class notes are Sections 4.1, 4.2, 4.3, and 5.1.

Problems: Please submit solutions to the following problems on Friday, March 27.

1.

For each sine wave, find the phasor representation (in polar form), and sketch the phasor in the complex plane.

(a)

$0.2 \cos ( 1000 t - 45^o )$

(b)

$7 \cos (10 t + 150^o)$

2.

For each phasor, express the corresponding sine wave as a time function, and sketch the sine wave versus time. Assume $\omega = 2 \pi 100$.

(a)

$\underline{v} = 7 \angle{0^o}$

(b)

$\underline{v} = 2 \angle{-90^o}$

3.

Find the magnitude of each complex number below.

(a)

$\underline{v}_1 = 1 + j1$

(b)

$\underline{v}_2 = 3 - j4$

(c)

$\underline{v}_1 + \underline{v}_2$

(d)

$(\underline{v}_1) \cdot (\underline{v}_2)$

[CONTINUED ON BACK OF PAGE]

Please submit solutions to the following problems on Monday, March 30.

1.

A circuit and its phasor/impedance equivalent are shown below. Determine the current i(t), and sketch i(t) versus t. Indicate the sine wave amplitude, frequency, and phase in the sketch. Note that $\frac{1}{j} = \frac{1 \angle{0^o}}{1 \angle{90^o}} = 1 \angle{-90^o} = -j$.

CIRCUIT OMITTED IN HTML DOCUMENT -- SEE PAPER COPY

2.

Classify each circuit below as one of the following types of filter: low-pass, high-pass, or band-pass. You can do this either by thinking about how each circuit operates as $\omega \rightarrow 0$ and $\omega \rightarrow \infty$,or you can analyze the circuits as voltage dividers with impedances and study the resulting equations.

CIRCUIT OMITTED IN HTML DOCUMENT -- SEE PAPER COPY