**Discrete Circuit Perspective**

For discrete electrical circuit components, a capacitor is typically made of a dielectric placed between conductors. The lumped element model of a capacitor includes a lossless ideal capacitor in series with a resistor termed the equivalent series resistance (ESR), as shown in the figure below. The ESR represents losses in the capacitor. In a low-loss capacitor the ESR is very small, and in a lossy capacitor the ESR can be large. Note that the ESR is *not* simply the resistance that would be measured across a capacitor by an ohmmeter. The ESR is a derived quantity representing the loss due to both the dielectric's conduction electrons and the bound dipole relaxation phenomena mentioned above. In a dielectric, only one of either the conduction electrons or the dipole relaxation typically dominates loss. For the case of the conduction electrons being the dominant loss, then

,

where is the lossless capacitance.

When representing the electrical circuit parameters as vectors in a complex plane, known as phasors, a capacitor's **loss tangent** is equal to the tangent of the angle between the capacitor's impedance vector and the negative reactive axis, as shown in the diagram to the right. The loss tangent is then

.

Since the same AC current flows through both *ESR* and *X _{c}*, the loss tangent is also the ratio of the resistive power loss in the ESR to the reactive power oscillating in the capacitor. For this reason, a capacitor's loss tangent is sometimes stated as its

*dissipation factor*, or the reciprocal of its

*quality factor Q*, as follows

.

Read more about this topic: Loss Tangent

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