EECS 210_________________________PROBLEM SET #7________________________Winter 2001

**ASSIGNED:** March 2, 2001. **Read:** Sects. 9.1-9.5 (skip Chaps. 7 & 8) and Appendix B of the text.

**DUE DATE:** March 9, 2001. **In Lab Book:** Read Unit #4, Lab Lecture #4 and Lab Experiment #4.

**THIS WEEK:** Inductors and capacitors and complex numbers.

- Text #6.4. Just apply the integral counterpart to v=L(di/dt), but watch units! Use Matlab for (b).

Note that inductor current must be continuous at t=0.001 and t=0.002 seconds--a useful check.
- Text #6.7. Compute
**numerical values** for A_{1} and A_{2}. Let x=e^{5000t} in (b)
- Text #6.19. Requires a nasty derivative; otherwise easy. You should already know answer to (c).
- Text #6.21. Combining inductors in series and parallel. All integers after the beginning.
- Text #6.26a-e. Careful on (c) and (d)--the initial currents must match the given values.

For each of the following pairs of complex numbers, do the following:
- Multiply them directly in rectangular form, getting an answer in rectangular form;
- Convert to polar form, multiply in polar form, convert product back to rectangular form.
- {4+j3,5+j12}; {4+j3,(5+j12)
^{*}}; {4+j3,1/(5+j12)}; {1/(4+j3),1/(5+j12)}; {(4+j3)^{*},(5+j12)}

- Show complex number [5(8+j)(8+j6)(5+j12)(5+j10)]/[26(7+j4)(7+j24)(2+j11)] has magnitude=1.

- Use trig identity from Problem Set #1 to show 5cos(3t+30°)+5sin(3t)+5cos(3t-210°)=0 exactly!

Now use phasor representations of the sinusoids to show it. Plot the phasors in the complex plane.

**Ungraded:** We are given two unmarked boxes, each with a pair of wires sticking out of it.

One contains the Thevenin equivalent of a circuit; the other contains its Norton equivalent.

Explain how to **distinguish** the Thevenin equivalent box from the Norton equivalent box.

HINT: This *cannot* be done using i-v characteristics of the two boxes; need something else.

"An optimist is an accordion player with a beeper"--Ted Koppel.