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Impedence

 

The impedance Z of a resistance R in series with a reactance X is:
Z = R + jX

Rectangular and polar forms of impedance Z:
Z = R + jX = (R2 + X2)½
Ðtan-1(X / R) = |Z|Ðf = |Z|cosf + j|Z|sinf

Addition of impedances Z1 and Z2:
Z1 + Z2 = (R1 + jX1) + (R2 + jX2) = (R1 + R2) + j(X1 + X2)

Subtraction of impedances Z1 and Z2:
Z1 - Z2 = (R1 + jX1) - (R2 + jX2) = (R1 - R2) + j(X1 - X2)

Multiplication of impedances Z1 and Z2:
Z1 * Z2 = |Z1|
Ðf1 * |Z2|Ðf2 = ( |Z1| * |Z2| )Ð(f1 + f2)

Division of impedances Z1 and Z2:
Z1 / Z2 = |Z1|
Ðf1 / |Z2|Ðf2 = ( |Z1| / |Z2| )Ð(f1 - f2)

In summary:
- use the rectangular form for addition and subtraction,
- use the polar form for multiplication and division.