Doubts about linear elements of electrical circuits

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SUMMARY

The discussion centers on the definitions and relationships of impedance, admittance, and their components in electrical circuits. Impedance (Z) is defined as Z = R + jX, while admittance (Y) is expressed as Y = G + jB, with susceptance (B) defined as B = (ωC - 1/ωL). The conversation also clarifies that conductance (G) can be defined as G = R/(R² + X²), which generalizes the reciprocal relationship when reactance (X) is zero. The participants emphasize the significance of sign conventions in reactance and the duality of electrical components.

PREREQUISITES
  • Understanding of complex numbers in electrical engineering
  • Familiarity with impedance and admittance concepts
  • Knowledge of reactance and its types (inductive and capacitive)
  • Basic principles of electrical circuits and their components
NEXT STEPS
  • Study the derivation and applications of the impedance formula in AC circuits
  • Explore the concept of susceptance and its role in circuit analysis
  • Learn about the significance of sign conventions in reactance and their implications
  • Investigate the duality principles in electrical components, including elastance and reluctance
USEFUL FOR

Electrical engineers, students studying circuit theory, and professionals involved in AC circuit analysis will benefit from this discussion.

brunotolentin.4
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First doubt: The impedance Z is defined how Z = R + j X and the reactance X can be wrote how:

69fce93e83daf93f03b01dbcfbf47065.png


Source: https://en.wikipedia.org/wiki/Electrical_reactance

So, by analogy, the admitance Y is defined how Y = G + j B and the susceptance B can be wrote how what? So:
B = \left( \frac{\omega C}{1} - \frac{1}{\omega L} \right)
Or this form:
B = \left( \frac{1}{\omega L} - \frac{\omega C}{1} \right)
?

Help: https://it.wikipedia.org/wiki/SuscettanzaSecond doubt: in this page: "https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance", the condutance G is defined how the reciprocal of R, BUT, BUT, in this page: "https://en.wikipedia.org/wiki/Susceptance", the condutance G is defined now how:
G = \left( \frac{R}{R^2+X^2} \right)
So, this last equation is the general definition of G and the first definition is the particular case, when X = 0, correct!?
 
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Hi,

About your first question, both forms differ only in the sign and since the reactance is a complex magnitude, the sign is not relevant.

As for your second question, I don't see in https://en.wikipedia.org/wiki/Susceptance the definition of G that you have written.Sergio
 
USeptim said:
Hi,

About your first question, both forms differ only in the sign and since the reactance is a complex magnitude, the sign is not relevant.

Exist a convention (maybe, can be that exist a good reason for this convention, but I don't know) for the signal of X, if X>0, thus the X is a indutive reactance and if X<0, thus X is capacitive reactance.

So, the duality of the capacitance is the elastance and the duality of the indutance is the relutance. So, by analogy, shoud exist a convention (or a deduction) for the signal of B too. What would be?
 
Last edited:

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