In this situation of positive, imaginary impedance, the impedance is purely inductive, as an ideal
inductor would be. The impedance of an ideal inductor with inductance L is a linear function of
frequency, given by Z
L
= jωL.
If the phase of the voltage is 90 degrees (π/2 radians) behind the phase of the current, then the
impedance is a negative imaginary number:
()
||
||
||
||
2/
I
V
je
I
V
Z
j
−==
−
π
(6)
In this situation of negative, imaginary impedance, the impedance is purely capacitive, as an ideal
capacitor would be. The impedance of an ideal capacitor with capacitance C is the inverse of a linear
function of frequency, given by Z
C
= 1 / jωC = −j /.ωC.
Actual circuit components are not purely resistive, inductive, or capacitive. From a practical
standpoint, capacitors and inductors have impedances with resistive parts, and their impedances
may not be linear functions of frequency or independent of the voltage. The general expression for
impedance, considers a real part containing the resistive component of the entire impedance, R, and
the reactance or imaginary part of the impedance, being X
l
, Xc, or the algebraic sum of the two. This
complex impedance is represented by:
Z = R + j X, (7)
Where X = ωL for an inductor and X = −1/ωC for a capacitor. Since the quantity X is traceable to the
ratio of a voltage to a current, it is expressed in ohms. Often, it is desirable to express the impedance
in ohms as a scalar (real) quantity; in that case, its magnitude
22
| XRZ +=| is used.
Units
The unit of resistance is the ohm, with the symbol Ω (omega). A 1-Ω resistor drops 1 volt across its
terminals when one Ampere is flowing through the resistor.
The unit of inductance is the Henry, with the symbol H. For a one-amp AC current, a 1-H inductor
would produce an AC voltage across it whose magnitude is numerically equal to 2π times the
frequency in Hertz.
The unit of capacitance is the Farad, with the symbol F. For a one-amp AC current, a 1-F
capacitor would produce an AC voltage across it whose magnitude is numerically equal to the inverse
of 2π times the frequency in Hertz.
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