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#1
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I GOT IT! I GOT IT! I GOT IT!
Thanks for all your help! I just wrote the exam with a 92% pass. The Eternal Squire |
#2
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From: on Aug 30, 3:38 pm
All, I'm an Advanced studying for my Extra, and so far I am getting 66% on the practice exams without even studying after about 3 years of homebrewing. I need a few extra points to make it over the top, and since I am a builder (of sorts) I would like to do it using the electrical principles part of the exam. However, the questions pool provides the answers but not how to get them. I'd rather be able to understand how to arrive at it without a calculator. You need some DEFINITIONS made clear first. See following... Problem class 1: impedance and phase angle of RLC parallel circuit where component values and frequency are known. Problem class 2: impedance and phase angle of RLC series circuit where component values and frequency are known. Could I calculate these graphically using tip-to-tail summation of impedance vectors? ...if you have some polar-coordinate graph paper, yes. From what I understand, |Z| = 2 pi F L, |Z| = 2 pi / (F C), |Z| = R WRONG. Impedance Z = Resistance R + j Reactance X for a series- resonant circuit. Further, X_L = 2 pi F L and X_C = -1 / (2pi F C). "|Z|" is MAGNITUDE of impedance; you can't do "phase calculations" using just magnitudes of either Z or Y. Note: Admittance Y is composed of conductance G = 1 / R (real part) and susceptances B_L = -1 / (2 pi F L) and B_C = 2 pi F C (imaginary part). But how can I get the phase angle or the conjugate pair so that I can do the vector addition? A "conjugate match" (or "pair") results when the magnitude of inductive reactance is exactly equal to the magnitude of capacitive reactance. Their relative phase angles are 180 degrees and opposed; they "cancel" each other. In a series-resonant circuit that leaves you with ONLY the RESISTIVE part of the complex number expression for impedance. |Z| = SQRT ( R^2 + X^2 ), Impedance phase PHA = Tan (X / R) You must assign a polarity to X in order to maintain relative phase angles. Capacitive reactance is assigned a negative value while inductive reactance is assigned a positive value. For admittance Y (such as with a parallel-resonant circuit), the magnitude (|Y|) is the same square-root of the sums of the squares (and thus always positive), but the inductive susceptance is negative and the capacitive susceptance is positive in value. Doing "vector plotting" is generally NOT a good short-cut way to get acquainted with either Y or Z...UNLESS you ALWAYS keep in mind the relative phase of inductance and the relative phase of capacitance...and forget the small frequency differences where reactance/susceptance of L is bigger/smaller than reactance/ susceptance of C. AT RESONANCE the angles are EQUAL in magnitude but opposed in phase; they equate to zero. The rules of arithmetic of the "rectangular form" of complex quantities is well-known and mentioned in all sorts of texts, including the mathematics handbooks. Going through numbers with rectangular form is no more harder/easier than trying to plot vectors with polar form representation. Assignment to the student: Learn the rectangular-form arithmentic rules for complex quantities. ANY text that has anything to say about complex quantities will have those rules. A hint to keep from re-inventing the wheel. The HP 32S and 33 scientific pocket calculators have both forms' arithmentic rules preprogrammed...AND they do both the real and imaginary part calculations and answer displays like right now. The HP 33 costs about $50 new. |
#3
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Len,
Thanks for your advice regarding the calculator. I found that the various questions are constructed to be answered correctly simply by using vector graphical methods, long division, and approximation of inputs for fast figuring. The Eternal Squire |