Calculating Capacitance and Inductance from Capacitive Reactance and Inductive Reactance
I'm trying to find the inductor (L) and capacitor (C) values using the inductive reactance (XL) and capacitive reactance (XC).
Edit: I also have the frequency (f=50 Hz).
I know \$XL = 2\pi f L\$ and I know \$XC = \dfrac{1}{2\pi f C}\$, but I am not the best at reversing formulas, I am still learning.
Can anyone confirm the correct formulas please?
I have tried assigning random values to each part of the equations, but my answers don't seem to match up for some reason. I don't know where I am going wrong, but nevertheless keen to learn and willing to ask.
I have also tried searching online, but the only articles I can find of relevance are about calculating XC and XL, not C and L from XC and XL.
Best Answer
Where
and you start with:
$$ X_L = 2 \ \pi \ f\ L, $$
then divide both sides of the equation by \$2\pi\ f\$ in order to isolate the \$ L\$, you'll get:
$$ \frac {X_L}{2 \ \pi \ f}= \frac{ \require{cancel} \cancel { 2 \ \pi \ f}\ L}{ \require{cancel} \cancel { 2 \ \pi \ f}}\text{ .} $$
Move the \$L\$ over to the left hand side and, like magic, Voila! $$ L= \frac{X_L}{2 \ \pi \ f}\ $$
Rearranging to get the capacitance, if you start with:
$$Xc = \frac{1}{2 \ \pi \ f\ C} $$
and multiply both sides of the equation by C, in order to put C in a less cumbersome place to work with, you'll get:
$$C\ X_C = \frac{1\require{cancel} \cancel {C}}{2 \ \pi \ f\require{cancel} \cancel {C}} $$
Finally, in order to isolate C and put the reactive term in its place, divide through by\$ X_C\$ and you'll get:
$$ \frac{C \require{cancel} \cancel {X_C}}{\require{cancel} \cancel {X_C}} = \frac{1}{2\pi\ f\ X_C}{ \text{ , }} $$ and after you clean it all up you'll have:
$$ C = \frac{1}{2\pi\ f\ X_C}$$