# Trying to find value of two capacitors using resonant frequencies in three conditions, but wrong formula is derived

I was trying to find capacitance of two capacitors in the following way.

• Connect each capacitor individually to a same inductor and find resonant frequency in each case.
• Connect the same capacitors in series , to the same inductor and find the resonant frequency.
• Then calculate the capacitance using following way

we have

$$\f_{1} = \frac{1}{2 \pi \sqrt{L c_{1}}}\$$ , $$\f_{2} = \frac{1}{2 \pi \sqrt{L c_{2}}}\$$, $$\f_{3} = \frac{1}{2 \pi \sqrt{\frac{L \left(c_{1} + c_{2}\right)}{c_{1} c_{2}}}}\$$

Solving these equations, we get

$$\\left\{ L : \frac{1}{4 \pi^{2} f_{3} \sqrt{f_{1}^{2} + f_{2}^{2}}}, \ c_{1} : \frac{f_{3} \sqrt{f_{1}^{2} + f_{2}^{2}}}{f_{1}^{2}}, \ c_{2} : \frac{f_{3} \sqrt{f_{1}^{2} + f_{2}^{2}}}{f_{2}^{2}}\right\}\$$

I tried to substitute the values for f1, f2 & f3 ( f1 = 2500, f2 = 2030, f3 = 3200 ) . Interestingly , I got a result which is numerically correct , but with a difference of $$\1e^{-6}\$$. That is, instead of micro farad, I get values in farad, Also, instead of millihenry, I get value in nanohenry

I was trying to figure out why this difference in occurred .

The completed IPython notebook can be found at https://gist.github.com/harish2704/5fe08c80c96307973a11f724a218950d

it will be a great help if someone can help me

• What were the actual measured frequencies? – user4574 Jul 9 '19 at 20:50
• @user4574: I edited the question with this info. – harish2704 Jul 9 '19 at 20:55
• Is the inductance known or are you trying to calculate it too? – Harry Svensson Jul 9 '19 at 20:59
• @HarrySvensson: I know capacitance of one of the capacitance. Thus, we can say inductance is also a known value – harish2704 Jul 9 '19 at 21:02