### Formulas

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 = (R ^{2} + X^{2})^{½}Ðtan^{-1}(X / R) = |Z|Ðf = |Z|cosf + j|Z|sinf**

Addition of impedances **Z _{1}** and

**Z**:

_{2}**Z**

_{1}+ Z_{2}= (R_{1}+ jX_{1}) + (R_{2}+ jX_{2}) = (R_{1}+ R_{2}) + j(X_{1}+ X_{2})Subtraction of impedances **Z _{1}** and

**Z**:

_{2}**Z**

_{1}– Z_{2}= (R_{1}+ jX_{1}) – (R_{2}+ jX_{2}) = (R_{1}– R_{2}) + j(X_{1}– X_{2})Multiplication of impedances **Z _{1}** and

**Z**:

_{2}**Z**

_{1}* Z_{2}= |Z_{1}|Ðf_{1}* |Z_{2}|Ðf_{2}= ( |Z_{1}| * |Z_{2}| )Ð(f_{1}+ f_{2})Division of impedances **Z _{1}** and

**Z**:

_{2}**Z**

_{1}/ Z_{2}= |Z_{1}|Ðf_{1}/ |Z_{2}|Ðf_{2}= ( |Z_{1}| / |Z_{2}| )Ð(f_{1}– f_{2})In summary:

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

NOTATION |
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The symbol font is used for some notation and formulae. If the Greek symbols for alpha beta delta do not appear here [ a b d ] the symbol font needs to be installed for correct display of notation and formulae. |
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BCEfGhIjLPQ |
susceptance capacitance voltage source frequency conductance h-operator current j-operator inductance active power reactive power |
[siemens, S] [farads, F] [volts, V] [hertz, Hz] [siemens, S] [1Ð120°] [amps, A] [1Ð90°] [henrys, H] [watts, W] [VAreactive, VArs] |
QRStVWXYZfw |
quality factor resistance apparent power time voltage drop energy reactance admittance impedance phase angle angular frequency |
[number] [ohms, W] [volt-amps, VA] [seconds, s] [volts, V] [joules, J] [ohms, W] [siemens, S] [ohms, W] [degrees, °] [rad/sec] |

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