Hints for Assignment 12

The hints below are very detailed, since there are many new things to learn here. If you get stuck following these suggestions, please send me a note telling me where and how. I will try to get you unstuck and modify the hints to help everyone else as well.

I will use "w" for omega everywhere in these hints.

58.

Analyze the circuit using the results obtained in class, and then get the potential drops by similar arguments [V=IZ].

Why is |VAC| <> |VAB| + |VBC| ? To address this question, write out the each of these voltages in the form V = |V|cos(wt+phi). Is the angle phi the same in each case?

59. In part (c), sketch the coefficient of the cosine, not the entire Vout

Because future problems are going to be harder, solve this problem by using complex impedances:

The problem is then done exactly as DC circuits are done, except that at the end, the voltage is given by the REAL PART of the algebraic answer. The starting equation is

      Vin = I Ztot = V0 exp(iwt) I Ztot

and you want the real part of the voltage drop across the resistor.

60. You might want to work this one both by solving the two differential equations and by using complex impedances, in order to see how the two methods wind up with the same answers. For the differential equations, the statement of the problem gives you the trial functions you need.

61. The amplitude of a current I = Im cos(wt + phi) is just |Im| , since amplitudes are not negative. The easiest way to find amplitudes is to convince yourself that in complex form,

      I = (Re Im + i Im Im ) exp(iwt)

the amplitude of the current is |Im| = sqrt [(Re Im2) + (Im Im2)], while the phase phi is just the phase of Im in the sense of complex numbers.

With this understanding of the amplitude of the current, you can use your intuition from DC circuits and the minimum-possible amount of algebra. Unfortunately, the minimum-possible amount of algebra can still be substantial, so you should use a symbolic-algebra package. Use your solution to problem 33 to help with this problem.

62. You will certainly need a symbolic-algebra package to help with this one. You can use your solution to problem 36 to help solve this problem.

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Last revised 1998/04/16