Electrical impedance

Electrical impedance is a physical quantity that represents the opposition force of a circuit to the passage of alternating electric current, or, more generally, of a variable current. In other words, is the amount of opposition that an electrical element offers to current flow in a circuit when a voltage is applied at a specific frequency. It can be expressed as a complex number and is given by the relationship between voltage and current.

Commonly the impedance is indicated by \(Z\), and its unit of measurement is the ohm \((\Omega)\).

The concept of impedance generalizes Ohm’s law extending it to circuits operating in a sinusoidal regime (commonly called alternating current): in fact, in a continuous current regime, it represents the electrical resistance. It takes into account the phenomena of electric current consumption and the phenomena of electromagnetic energy accumulation.

The electrical impedance is described mathematically by a complex number, whose real part in the schematization with elements in series represents the dissipative phenomenon and corresponds to the electrical resistance, \(R\). While the imaginary part, called reactance, \(X\), is associated with the energy phenomena of accumulation.

\[\dfrac{V}{I}=Z=R+jX\]

The reciprocal of impedance is called admittance \(Y\).

How to calculate electrical impedance

To calculate the impedance of a capacitor, the formula to do so is:

\[Z_C=\dfrac{1}{2\pi fC}\]

where \(Z_C\) is the impedance in unit ohms, \(f\) is the frequency of the signal passing through the capacitor, and \(C\) is the capacitance of the capacitor. To calculate the impedance of an inductor, the formula to do so is:

\[Z_L=2\pi fL\]

where \(Z_L\) is the impedance in unit ohms, \(f\) is the frequency of the signal passing through the inductor, and \(L\) is the inductance of the inductor. If there are both capacitors and inductors present in a circuit, the total amount of impedance can be calculated by adding all of the individual impedances:

\[Z_{tot}=Z_C+Z_L\]

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