Aug 282014
 

Impedance (Z) = R + jX

Impedance is the phasorial addition of resistance and reactance.

The resistance is the opposition’s value to the flow of the electric current (whether direct current or alternating current). The reactance is the opposition’s value to the flow of the alternating current through a capacitor or inductor.

The opposition to the alternating current in a capacitor is called capacitive reactance and the opposition to the alternating current in an inductor is called inductive reactance.

When these elements (resistors, capacitors and inductors) are combined in the same circuit and an alternating current flows through them, the opposition of this set of elements to the flow of the alternating current is called Impedance. The Impedance unit is Ohms, and it is equal to the addition of a resistive value (resistance) and a reactive value due to a reactive components (inductors and capacitors): Z = R + jX.

Impedance (Z) = (Resistance + Reactance)

The “j” letter that goes before the X, tells us that the X is an imaginary number. This is not a common addition, It is a phasorial addition (sum of phasors).

What happens is that these elements (the inductor and the capacitor) cause an opposition to the flow of the alternating current (plus a phase difference), but they do not ideally cause any dissipation of power, as the resistor (Joule’s Law).

There is a phase difference between the voltage and the current that flows through the capacitor and through the inductor. The voltage gets behind the current on the capacitor. The current gets behind the voltage on the inductor.

This phase difference on the inductor and the capacitor is opposites, and if they have the same magnitude, they would be cancelled and the total impedance of the circuit would be equal to the value of resistor. (see the formula above).

The previous formula is represented by the picture above. You can see that the reactances are on the y-axis (the imaginary axis) and they may go up or down, depending on wish influence is higher the one of the capacitor or the one of the inductor, and resistance is always on the X-axis. (It is only on the positive side).

The value of the impedance (the diagonal line) is: Z = (R2 + X2)1/2.

Note: The parentheses to 1/2 power is equal to a square root.

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