Series RLC circuits:
When the coil, capacitor, and resistor are connected in series, the resistance R can be thought of as all belonging to coil, when you use above formulas. (Thinking of it all as belonging to capacitor will work.) Then you have 2 vectors to add, while finding the impedance of a series RLC circuit:
Z = (R + jXL) +(0 +jXC)
= R + j(XL+ XC)
Figure-- A series RLC circuit.
A resistor, coil, and capacitor can be connected in series with R =50 Ω, XL=22 Ω, and XC -33 Ω. What is net impedance, Z?
Consider resistor to be part of the coil, obtaining 2 complex vectors, 50+j22 and 0-j33. Adding all these gives the resistance component of 50 + 0 = 50, and the reactive component of j22-j33 =-j11. Thus, Z= 50 - j11.