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Formula for Q of resonant circuit?
On Feb 25, 4:40ï¿½pm, M J Dowden wrote:
I have been using *Q = (2 * Pi * f * L) / R, That's the formula for Q in a series resonant circuit. It's upside down from what you need for a parallel resonant circuit. What you need is this formula, which is used for parallel RLC circuits: Qp = R / (2 * Pi * f * L) It's easy to remember which to use if you consider that in a parallel resonant circuit, increasing the resistance in parallel with L and C increases the Q. In a series resonant circuit, *decreasing* the resistance in series with L and C increases the Q. but the questions in section E5G of the test pool don't seem to work with that. Try again with the formula above. Some simplifications help, too: 1) There are combinations of units that result in exponents cancelling. For example, MHz times microhenries is 10^6 times 10^6, effectively eliminating them from the calculation. 2) 2 * pi is 6.28 for almost all work. 3) The inductive reactance, aka XL, is (6.28 * f * L). E5G01 (A) What is the Q of a parallel RLC circuit if the resonant frequency is 14.128 MHz, L is 2.7 microhenrys and R is 18 kilohms? First we figure out XL XL = 6.28 * 14.128 * 2.7 Since we are dealing in microhenries and megahertz, the 10^6 and 10^6 exponents cancel out, and XL = 239.5 ohms. Then we divide R, which is 18,000 by XL, which is 239.5 ohms Answer: 75.15 The choices on the exam a A. 75.1 B. 7.51 C. 71.5 D. 0.013 Clearly the answer is A. The answer isn't exact because of rounding of 6.28 and 239.5. Try some others in the pool. 73 de Jim, N2EY 
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