# In an $RLC$ circuit, where there are multiple components instead of a single resistor/inductor/capacitor how does impedance $Z$ is calculated?

If there is an $$RLC$$ circuit where some components are in series with one another and some components are in parallel with one another, how does the total impedance of the circuit is calculated?
I understand that the components that are in series will have their current in phase, while those that are in parallel will have their voltage in phase. All these different phases make me dizzy to operate on the circuit. How to approach these kinds of questions and are there any advices for students who are new to this concept?

My senior told me to use second-differential equation to solve it, but since I haven't learned that, my teacher told me to use phasor diagram to solve these kinds of questions.

• Do you know how to calculate series and parallel combinations of resistors? Do you know the mesh and node analysis methods for general resistive circuits? Apr 18, 2023 at 15:39
• Yes I have both series and parallel combinations of resistors, and the mesh and node analysis, but I don't think this will help in calculating the phase angle of each impedance..? or im wrong im not sure Apr 18, 2023 at 19:40

$$Z_C = \frac{1}{j\omega C}$$ or $$Z_L = j\omega L$$ where $$j$$ is the unit imaginary number, and $$\omega$$ is the source frequency.
Now just take the phase of your resulting impedance. If you have a complex number $$a+jb$$, the phase is just $${\rm atan}\frac{b}{a}$$, plus possibly adding $$\pi$$ to account for which quadrant the number is in, which you can determine from the signs of $$a$$ and $$b$$.
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