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What is the resonant frequency of a 10-mH inductor and a 0.005-uF capacitor?They showed...
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The resonant frequency of a series or parallel alternating LC circuit is the same. It can be computed from the resonance condition which is (for a series circuit) the equality of voltage drops on the inductor and capacitor or (for a parallel circuit) the equality of currents through the inductor and capacitor. This equality reduces, in turn, to the condition of their reactances being equal. X(L)= X(C)
`omega*L = 1/(omega*C)` where `omega =2*pi*F`
This leads to a value for the resonant frequency of
`F = 1/(2*pi*sqrt(L*C))`
For the values given in text of L=10 mH and C=0.005 microF=5 nF (and having `pi` correct up to 25 decimals) one has
`F =1/(2*pi*sqrt(0.01*5*10^(-9))) =22507.9 Hz=22508 Hz =22.5 kHz`
Posted by valentin68 on September 7, 2013 at 3:06 AM (Answer #1)
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