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A tank circuit uses a 0.09 uH inductor and a 0.4-uF capacitor. What would the resonat...

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t4trendesetter | Honors

Posted September 7, 2013 at 5:15 PM via web

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A tank circuit uses a 0.09 uH inductor and a 0.4-uF capacitor. What would the resonat frequency be?

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valentin68 | College Teacher | (Level 3) Associate Educator

Posted September 7, 2013 at 5:54 PM (Answer #1)

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No matter if the resonant (or other said, tank) circuit is parallel or series the resonance condition is the same, that is the currents (or voltages) on the inductor and capacitor cancel each other. This, in turn leads to the equality of component reactances X(C) = X(L)

Because `X(C) = 1/(omega*C)` and `X(L) = omega*L` the above equality writes as (at resonance)

`1/(omega_r*C) = omega_r*L`  or `omega_r = 1/sqrt(L*C)`

Now, the general relation between angular frequency `omega` and frequency F itself is

`omega =2*pi*F`

which gives a value for the resonant frequency

`F_r = 1/(2*pi*sqrt(L*C)) = 1/(2*pi*sqrt(9*10^(-8)*4*10^(-7)))= `

`=838.82*10^3 Hz =838.82 KHz`

The resonant frequency is 838.82 KHz.

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