The Impedance Z in an AC circuit is a generalized measure of the ohmic resistance of a circuit element or a combination of circuit elements. The units of Impedance is always in ohms, W.
The impedance can be used to find the emf (or voltage) across some circuit component (or combination of components) using a equation that has the same structure as Ohm's Law.
In words: The voltage across a circuit element at some moment t can be found by multiplying the element's Inpedance Z times the current not at that monent t but the current evaluated at some other time that is either ahead or behind the current moment by a time t. The time shift t can be determined once the phase angle is f known.
The Impedances of a capacitor or an inductor are frequency dependent, while that of a resistor is constant.
Circuit Element(s)
Impedence (W)
Phase Angle (f)
Z = R
0o
Z = XL = wL
+90o
Z = XC =1/wC
-90o
0o < f < 90o
-90o < f < 0o
f > 0o if XL > XC f = 0o if XL = XC (Resonance) f < 0o if XL < XC
Voltage and Current Phase Angle Relationships
The following is a visual derivation of the general inpedance and phase angle equations:
The last figure shows the phase relationship between the voltages across different circuit components and total voltage across the whole circuit. Observe that the current is in phase with the resistor.
