Consider the LC circuit. If one needs to tune this circuit to a frequency of 84 kHz, and the capacitor has a capacitance C = 3.0 mF, what inductance L is needed?

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1 Answer
May 1, 2018

The resonant frequency of an LC circuit occurs when the capacitive reactance equals the inductive reactance:

#X_C = X_L#

Substitute #X_C = 1/(2pifC)#:

#1/(2pifC) = X_L#

Substitute #X_L = 2pifL#:

#1/(2pifC) = 2pifL#

Solve for L:

#L = 1/(4pi^2f^2C)#

Substitute #f = 84xx10^3" Hz"#:

#L = 1/(4pi^2(84xx10^3" Hz")^2C)#

NOTE: There is an error in the wording of this problem; it specifies that #C = 3.0" mF"# but the given answer implies that the capacitance must be #C = 3.0" "mu"F"#

Substitute #C = 3.0xx10^-6" F"#:

#L = 1/(4pi^2(84xx10^3" Hz")^2(3.0xx10^-6" F"))#

#L ~~ 1.2xx10^-6" H"#