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In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. [1]Quantitatively, the impedance of a two-terminal circuit element is the ratio of the complex representation of the sinusoidal voltage between its terminals, to the complex representation of the current flowing through it. [2]
The loss tangent is defined by the angle between the capacitor's impedance vector and the negative reactive axis. If the capacitor is used in an AC circuit, the dissipation factor due to the non-ideal capacitor is expressed as the ratio of the resistive power loss in the ESR to the reactive power oscillating in the capacitor, or
When using the Laplace transform in circuit analysis, the impedance of an ideal capacitor with no initial charge is represented in the s domain by: = where C is the capacitance, and; s is the complex frequency.
In the special case of entirely zero admittance or exactly zero impedance, the relations are encumbered by infinities. However, for purely-reactive impedances (which are purely-susceptive admittances), the susceptance is equal to the negative reciprocal of the reactance , except when either is zero.
Combining the equation for capacitance with the above equation for the energy stored in a capacitor, for a flat-plate capacitor the energy stored is: = =. where is the energy, in joules; is the capacitance, in farads; and is the voltage, in volts.
The complex generalization of resistance is impedance, usually denoted Z; it can be shown that for an inductor, = and for a capacitor, =. We can now write, V = Z I {\displaystyle V=Z\,I} where V and I are the complex scalars in the voltage and current respectively and Z is the complex impedance.
Figure 3: Resistor/capacitor voltage divider. Consider a divider consisting of a resistor and capacitor as shown in Figure 3. Comparing with the general case, we see Z 1 = R and Z 2 is the impedance of the capacitor, given by = = ,
Impedance extends the concept of Ohm's law to AC circuits, and possesses both magnitude and phase at a particular frequency, unlike resistance, which has only magnitude. Impedance is a measure of the ability of the capacitor to pass alternating currents. In this sense impedance can be used like Ohms law