# What is the resonant frequency of a 10-mH inductor and a 0.005-uF capacitor?They showed me how they got their answer fr=(1/6.28(sq rt of LC) ) but when I do it I don't get their exact answer which is 22,500Hz or 22.5kHz

valentin68 | College Teacher | (Level 3) Associate Educator

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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`

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