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Old February 26th 07, 01:42 AM posted to rec.radio.amateur.moderated
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Default Formula for Q of resonant circuit?

On Feb 25, 4:40�pm, 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 R-L-C 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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