Question

How is impedance calculated?

Answer 1

Impedance is a measure of the opposition that a circuit offers to the flow of alternating current (AC). It takes into account both resistance and reactance, where reactance represents the opposition due to capacitance or inductance in the circuit. Impedance is denoted by the letter "Z" and is a complex quantity, meaning it has both a magnitude and a phase angle.

The formula for calculating impedance depends on the type of circuit component involved:

For a pure resistance (R):
Impedance (Z) = R

For a pure inductor (L):
Impedance (Z) = jωL
where:
j is the imaginary unit (sqrt(-1)),
ω is the angular frequency of the AC signal in radians per second, and
L is the inductance of the inductor in henries.

For a pure capacitor (C):
Impedance (Z) = -j / (ωC)
where:
j is the imaginary unit (sqrt(-1)),
ω is the angular frequency of the AC signal in radians per second, and
C is the capacitance of the capacitor in farads.

For a combination of resistance, inductance, and capacitance:
Impedance (Z) = √(R^2 + (X_L - X_C)^2)
where:
X_L = ωL is the inductive reactance, and
X_C = 1 / (ωC) is the capacitive reactance.

It's important to note that impedance is a vector quantity, and its phase angle indicates the phase relationship between the voltage and current in the AC circuit. The phase angle is calculated using trigonometric functions based on the ratio of reactance to resistance.

Keep in mind that impedance calculations are specific to AC circuits, as impedance is not relevant in direct current (DC) circuits where there is no frequency component. Also, when working with complex impedances, you may need to perform vector arithmetic or use complex number operations to determine the total impedance of a circuit.