EECS 210_________________________PROBLEM SET #7________________________Winter 2001

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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.

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THIS WEEK: Inductors and capacitors and complex numbers.

1. 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.
2. Text #6.7. Compute numerical values for A₁ and A₂. Let x=e^5000t in (b)
3. Text #6.19. Requires a nasty derivative; otherwise easy. You should already know answer to (c).
4. Text #6.21. Combining inductors in series and parallel. All integers after the beginning.
5. Text #6.26a-e. Careful on (c) and (d)--the initial currents must match the given values.

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6. 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)}

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

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8. 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.

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9. 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.

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