Calculating resonant frequency:
The formula for computing resonant frequency fo, in the terms of inductance L in henrys and capacitance C in farads, is
fo = 0.159/(LC)1/2
The half power is the square root.
If you are having the values L and C in henrys and farads, and you want to find out fo, do these calculations in this order: First, find out product LC, then take square root, then divide by 0.159 value. The result we obtain is fo in hertz.
The formula will work to find fo in megahertz, when L is given in micro henrys and C is in microfarads. These values are much more common than hertz, henrys, and farads in the electronic circuits. Remember that millions of hertz go with the millionths of henrys and millionths of farads.
This formula works for series-resonant and parallel-resonant both RLC circuits.
Problem:
Find out the resonant frequency of the series circuit with an inductance of 100 µH and a capacitance of 100 pF.
First, convert capacitance to microfarads: 100 pF = 0.000100 µF. Then find out the product LC = 100 x 0.000100 = 0.0100. Take square root of this, getting 0.100. And finally, divide 0.159 by 0.100, getting fo = 1.59 MHz.