# The equivalen reactance of an inductor and a capacitor

In my text book, I came across a problem where I needed to determine the equivalent reactance of a capacitor and an inductor (its ohmic resistance is negligible). To solve my problem I started to determine the equivalent reactance of both of them and to neglect the ohmic resistance of the inductor, and I thought of doing this:

Z = √Xl²−Xc². (Where: Z is the impedance, Xl is the inductive reactance and Xc is the capacitive reactance.)

But in the problem statement, Xc is 3Xl. So, putting them in the above equation is like:

Z =√Xl²-9Xl² =√-8Xl²

Which has no sense because of the negative sign. So my question is: What would be the equivalent reactance of an inductive and capacitive reactance? Is my approach correct but missing something, or it is wrong?

• The impedance is a complex number. So you should use complex math with addition and subtraction, that's it. – Marko Buršič Mar 23 '17 at 14:25
• You should read into what is called "complex numbers". – 12Lappie Mar 23 '17 at 14:26
• $X_C$ = 3$X_L$. So Z = $X_{NET}$ = $X_C$ - $X_L$ = 3$X_L$ - $X_L$ = 2$X_L$. As for the complex numbers, go there if you understand how it applies. But most circuits can be solved using trigonometry and pythagoras. – StainlessSteelRat Mar 23 '17 at 15:23