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
Best Answer
The formula for the series capacitors should be C1 * C2 / (C1 + C2). You have it upside down.