How to calculate reactance in a circuit full of coils?

Question

I've seen plenty of examples on how to calculate reactance with a combination of a coil, capacitor and ohmic resistor. However, I'm not sure how to find the overall reactance in a circuit that would look the following. We have AC and 3 coils where one coil is parallel to a series of the two other coils. Now I have 2 ideas.

Does $ frac{1}{X}= frac{1}{X_1} + frac{1}{X_2+X_3}$ for the parallel connection work?

The other one would be to calculate the overall inductance of the coils, $frac{1}{L}= frac{1}{L_1} + frac{1}{L_2+L_3}$ and then from there use the usual $X=2pi fL$.
Many thanks in advance

relayman357 · Answer

Reactances in series add like resistors in series, in parallel they combine like resistors in parallel.
Series:  $X_{equiv} = X_1 + X_2$
Parallel: $X_{equiv} = frac{1}{frac{1}{X_1}+frac{1}{X_2}}$
If inductive reactance, then it has a j operator to indicate its impedance at the particular steady-state frequency has angle of 90 degrees.  If capacitive reactance it has a -j operator (-90 degrees).
Combine the two that are in series first, then you will be left with 2 in parallel that you can combine.

How to calculate reactance in a circuit full of coils?

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