Admittance is the reciprocal of impedance. But:

1) Susceptance is the reciprocal of reactance, or the imaginary part of admittance ?

2) Conductance is the reciprocal of resistance, or the real part of admittance?

  • 2
    \$\begingroup\$ This is answered on the Wikipedia page on susceptance. \$\endgroup\$ – The Photon Jun 20 at 16:51

1) Both, susceptance is the reciprocal of reactance also is the imaginary part of an admittance, because admittance is the reciprocal of the impedance.

2) Both, conductance is the reciprocal of resistance and again as 1) is the real part of the admittance.

  • \$\begingroup\$ Do these definitions coincide for any kind of circuit we may consider? \$\endgroup\$ – Kinka-Byo Jun 20 at 16:12
  • \$\begingroup\$ Yes for any kind, when you try to calculate the input admittance of any circuit, because it has a lot of elements in paralell (just adding admittances in parallel).If you get the reciprocal of that admittance you get the input impedance of the circuit. \$\endgroup\$ – EduardoG Jun 20 at 16:20
  • \$\begingroup\$ What I do not understand is this: consider Z = R + jX. If we calculate the admittance Y = 1/Z, we get, after some calculus, Y = (R/(R^2 +X^2)) + j (-X/(R^2 + X^2)). And if we define susceptance and conductance as its imaginary and real parts, we get different expressions with respect to their other definitions (reciprocal of reactance and reciprocal of resistance). \$\endgroup\$ – Kinka-Byo Jun 20 at 16:31
  • \$\begingroup\$ yes you are right, that's because complex numbers properties ( you need to find Y = Z^-1 to get Z * Y = 1, of course that means that Y is not equal to 1/R + 1/jX. But when you have only a reactance (for example a simple inductor) Z = jX you have that Z^-1 = 1/jX. The rule of thumb would be that you always have to get the reciprocal of the impedance and/or the reciprocal of admittance. \$\endgroup\$ – EduardoG Jun 20 at 16:41
  • \$\begingroup\$ Just think about it as when you are getting the admittance from an impedance, considering Z = R+jX, you are getting the reciprocal of resistance ( susceptance) and the reciprocal of reactance (susceptance) of that impedance. It's not the same as getting the reciprocal of reactance (susceptance) of that impedance taking R = 0 and getting the reciprocal of resistance (conductance) of that impedance taking X = 0; \$\endgroup\$ – EduardoG Jun 20 at 17:10

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