Complex Variables and Material Constants

The current in the capacitor wire i = uY =uG - - juwC. The conductance G and the ciurent uG comprises all components that are in-phase with u. G is due both to DC conductance and AC losses in the dielectric. The j indicates that the uwC current is in quadrature (90° phase shifted) with u, it is a displacement current. AC losses and permittivity e are usually frequency-dependent, but even then Y is usually equal to (AZd)a at low frequencies. 

It may be useful to treat a and e as complex quantities in the time domain (e.g., to incorporate dielectric losses and frequency dependence). We then define  

Complex permittivity is used when the material is considered as a dielectric (an insulator) with losses. The capacitor is characterized with a complex capacitance or a complex permittivity  

Usually G is a real number in the equation Y = G + jB, but now G is considered complex = G = Y, thus taking care also of B. Then a = we [S/m], diverging as f oo (in contrast to e ). This is why ct for electrolytic materials may be a less attractive parameter. 

Use of specific resistance and specific conductance for resistivity and conductivity is not recommended. Resistivity has the unit [Qm], hut specific means a quantity per mass, so specific resistance should then have been [Q/kg]. 

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