impedance and admittance

rw combining impedances and admittances in series and parallel understanding the phase angle quality factor

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impedance

Impedance Z is essentially the ratio of the voltage across a circuit element to the current through it when we are dealing with sinusoidal signals. It is resistance generalized for AC. Z=V/I. Of course these are in phasors, frequency domain

Z = V/I = R + jX

1. The jX term in the impedance equation Z = V/I = R + jX represents the imaginary part of the impedance, called reactance
2. Reactance, like resistance, is measured in ohms. However, unlike resistance (which dissipates energy as heat), reactance stores energy in either an electric field (in a capacitor) or a magnetic field (in an inductor).
3. The j is used as a mathematical tool to represent the 90-degree phase shift between voltage and current in reactive components. It allows us to handle this phase difference using complex number arithmetic. Check capacitor and inductance in frequency domain

admittance

Y = I / V = G + jB

• This equation shows two important things:
  1. It restates the basic definition of admittance (Y = I/V).
  2. It decomposes admittance into its real and imaginary components:
     • G: Conductance (the real part). Conductance is related to how easily a circuit conducts current in phase with the voltage. For a purely resistive circuit, G = 1/R. However, G is not simply 1/R if there’s also reactance.
     • B: Susceptance (the imaginary part). Susceptance is related to how easily a circuit allows current flow that is out of phase with the voltage (due to energy storage in capacitors and inductors).
     • j: The imaginary unit, indicating the 90-degree phase shift associated with susceptance.

the table

questions

resonance

Resonance occurs at a particular resonance frequency, that is when the imaginary parts of impedances or admittances of circuit elements cancel each other.