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Electronics Reference

AC Circuits

Passive Elements Impedances and Admittances

Element
Impedance (Ohms, Ω)
Admittance (Siemens, S)
Resistor
latex!encoded:base64,XHRleHRybXtafT1cdGV4dHJte1J9
latex!encoded:base64,XHRleHRybXtZfT1cZnJhY3sxfXtcdGV4dHJte1J9fQ==
Inductor
latex!encoded:base64,XHRleHRybXtafT1qXG9tZWdhIFx0ZXh0cm17TH0=
latex!encoded:base64,XHRleHRybXtZfT1cZnJhY3sxfXtqXG9tZWdhIFx0ZXh0cm17TH19
Capacitor
latex!encoded:base64,XHRleHRybXtafT1cZnJhY3sxfXtqXG9tZWdhIFx0ZXh0cm17Q319
latex!encoded:base64,XHRleHRybXtZfT1qXG9tZWdhXHRleHRybXtDfQ==

The opposition of a circuit to the flow of a sinusoidal current is called impedance. It is the ratio of the phasor voltage (V) to the phasor current (I), measured in ohms (Ω). The impedance of a resistor, inductor, and capacitor can be determined using the equations above. Admittance (Y) is the inverse of impedance which is measured in siemens (S).

 > Passive Elements Impedances and Admittances

 

Circuit Impedance

latex!encoded:base64,XHRleHRybXtafT1cdGV4dHJte1J9K2pcdGV4dHJte1h9PVxsZWZ0IHwgXHRleHRybXtafSBccmlnaHQgfFxhbmdsZSBcVGhldGE=
latex!encoded:base64,XGxlZnQgfCBcdGV4dHJte1p9IFxyaWdodCB8ID0gXHNxcnR7XHRleHRybXtSfV57Mn0rXHRleHRybXtYfV57Mn19XDtcO1w7XDtcO1w7XDtcVGhldGEgPVx0ZXh0cm17dGFufV57LTF9XGZyYWN7XHRleHRybXtYfX17XHRleHRybXtSfX0=
latex!encoded:base64,XHRleHRybXtSfT1cbGVmdCB8IFx0ZXh0cm17Wn0gXHJpZ2h0IHwgXHRleHRybXtjb3N9XDtcVGhldGFcO1w7XDtcO1w7XDtcO1x0ZXh0cm17WH09XGxlZnQgfCBcdGV4dHJte1p9IFxyaWdodCB8IFx0ZXh0cm17c2lufVw7XFRoZXRh

The impedance of a circuit can be expressed in rectangular form Z=R+jX where R is the resistance and X is the reactance. It can be also expressed in polar form Z=|Z|∠θ.

 > Circuit Impedance

 

Series RLC Equivalent Impedance

Series RLC Equivalent Impedance
latex!encoded:base64,XHRleHRybXtafV97XHRleHRybXtlcX19PVx0ZXh0cm17Wn1fXHRleHRybXtSfStcdGV4dHJte1p9X1x0ZXh0cm17TH0rXHRleHRybXtafV9cdGV4dHJte0N9PVx0ZXh0cm17Un0ralxvbWVnYSBcdGV4dHJte0x9K1xmcmFjezF9e2pcb21lZ2EgXHRleHRybXtDfX1cO1w7KFx0ZXh0cm17T2htc30sIFxPbWVnYSk=

The total or equivalent impedance of series impedances is the sum of the individual impedances.

 > Series RLC Equivalent Impedance

 

Parallel RLC Equivalent Impedance

Parallel RLC Equivalent Impedance
latex!encoded:base64,XHRleHRybXtafV97XHRleHRybXtlcX19PVxmcmFjezF9e1xmcmFjezF9e1x0ZXh0cm17Wn1fXHRleHRybXtSfX0rXGZyYWN7MX17XHRleHRybXtafV9cdGV4dHJte0x9fStcZnJhY3sxfXtcdGV4dHJte1p9X1x0ZXh0cm17Q319fT1cZnJhY3sxfXtcZnJhY3sxfXtcdGV4dHJte1J9fStcZnJhY3sxfXtqXG9tZWdhIFx0ZXh0cm17TH19K2pcb21lZ2EgXHRleHRybXtDfX1cO1w7KFx0ZXh0cm17T2htc30sIFxPbWVnYSk=

The total or equivalent impedance of parallel impedances is determined by inverting the sum of the inverses of all impedances.

 > Parallel RLC Equivalent Impedance

 

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