Electrical impedance

Electrical impedance is an extension of the term electrical resistance to situations where an alternating current passes through an area. The simplest view of impedance is that it is the resistance to an alternating current. The base unit of impedance is ohm &Omega;, usually denoted by the letter Z. If the impedance is connected to a voltage U and a current I flows through it, its value is given the Ohm's law:
 * $$Z=\frac{U}{I}$$

Impedance of electrical elements
Essential electrical elements are resistor, capacitor a inductor. The primary property of a resistor is electrical resistance, the primary property of a capacitor is capacitance, and the primary property of an inductor is inductance. These are of course only ideal models, to emphasize this fact, only these particular terms are used and not the technical names officially given: resistor, capacitor and coil.

When calculating impedance, the frequency f is usually not used, but the circular frequency &omega; determined by the relation:
 * $$\omega = 2\pi\cdot f$$

Impedance of the resistor
The impedance of the resistor itself is called resistance, denoted R. The resistance value does not depend on the frequency.

Impedance of the capacitor
Impedance of the capacitor is called capacitance, normally denoted by XC. The capacitance is inversely proportional to the capacitance C of the capacitor ind inversely proportional to the frequency f of the applied voltage:
 * $$X_C = \frac{1}{\omega C}$$

Impedance of the inductor
Impedance of the inductor is called inductance, usually denoted by XL. Inductance is directly proportional to the inductance L of the inductor and directly proportional to the frequency f of the current flowing through the inductor:
 * $$X_L = \omega L$$

Impedance of series connection of resistor and capacitor
Addition of impedances is not done easily, for the impedance Z of the series connection of the resistor R and capacitor C goes:
 * $$Z = \sqrt{R^2 + \frac{1}{(\omega C)^2}}$$

Impedance of parallel connection of resistor and capacitor
The relation for the impedance Z of a resistor and capacitor in parallel connection has a rather complex form, but it is worth noticing because the parallel connection of a resistor and capacitor is a frequently used model for a tissue impedance:
 * $$Z = \frac{\sqrt{R^2 + \omega^2C^2R^4} }{\omega^2C^2R^2 + 1}$$

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