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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