While Ohm's Law applies directly to resistors in DC or in AC circuits, the form of the current-voltage relationship in AC circuits in general is modified to the form:
where I and V are the rms or "effective" values. The quantity Z is called impedance. For a pure resistor, Z = R. Because the phase affects the impedance and because the contributions of capacitors and inductors differ in phase from resistive components by 90 degrees, a process like vector addition (phasors) is used to develop expressions for impedance. More general is the complex impedance method.
Impedance Combinations
Combining impedances has similarities to the combining of resistors, but the phase relationships make it practically necessary to use the complex impedance method for carrying out the operations. Combining series impedances is straightforward:
Combining parallel impedances is more difficult and shows the power of the complex impedance approach. The expressions must be rationalized and are lengthy algebraic forms.
Parallel Impedance Expressions
The complex impedance of the parallel circuit takes the form
when rationalized, and the components have the form
where I and V are the rms or "effective" values. The quantity Z is called impedance. For a pure resistor, Z = R. Because the phase affects the impedance and because the contributions of capacitors and inductors differ in phase from resistive components by 90 degrees, a process like vector addition (phasors) is used to develop expressions for impedance. More general is the complex impedance method.
Impedance CombinationsCombining impedances has similarities to the combining of resistors, but the phase relationships make it practically necessary to use the complex impedance method for carrying out the operations. Combining series impedances is straightforward:
Combining parallel impedances is more difficult and shows the power of the complex impedance approach. The expressions must be rationalized and are lengthy algebraic forms.
Parallel Impedance ExpressionsThe complex impedance of the parallel circuit takes the form
when rationalized, and the components have the form
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