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Electrical Impedance

Published on 19/10/2018 and last updated on 20/10/2018
The current lags 90° (electrical) in respect of the applied voltage in a purely inductive circuit. The current leads 90° (electrical) in respect of the applied voltage in a purely capacitive circuit. The current does not lag as well as not lead in respect to the applied voltage in a purely resistive circuit. In a practical circuit where both inductive reactance and capacitive reactance present along with resistance or either of capacitive or inductive reactance presents along with resistance, there will be leading or lagging effect on the current of the circuit depending on the value of reactance and resistance of the circuit. In the AC circuit, the cumulative effect of reactance and resistance is termed as impedance. The impedance is normally denoted by English letter Z. The value of impedance is represented as Where R is the value of circuit resistance and X is the value of circuit reactance. The angle between applied voltage and current is The inductive reactance is taken as positive and capacitive reactance is taken as negative.

Impedance can be represented in complex form. This is Impedance The real part of a complex impedance is resistance and the imaginary part is reactance of the circuit.

Let us apply a sinusoidal voltage Vsinωt across a pure inductor of inductance L Henry. The expression of current through the inductor is From the expression of the waveform of the current through the inductor it is clear that the current lags the applied voltage by 90° (electrical).

Now let us apply same sinusoidal voltage Vsinωt across a pure capacitor of capacitance C farad. The expression of current through the capacitor is From the expression of the waveform of the current through the capacitor it is clear that the current leads the applied voltage by 90°(electrical).

Now we will connect the same voltage source across a pure resistance of value R ohm. Here the expression of current through the resistance would be From that expression, it can be concluded that the current has the same phase with the applied voltage.

Impedance of a Series RL Circuit

Let us derive the expression of the impedance of a series RL circuit. Here resistance of value R and inductance of value L are connected in series. The value of reactance of the inductor is ωL. Hence the expression of impedance in complex form is The numerical value or mod value of the reactance is

Impedance of a Series RC Circuit

Let us connect one resistance of value R ohm in series with a capacitor of capacitance C farad. The reactance of the capacitor is 1 / ωC. The resistance R and reactance of the capacitor are in series the expression of the impedance can be written as The mod value of the impedance of the series RC circuit is

Impedance of a Parallel RL Circuit

Here the resistance and inductor are connected in parallel. Here reciprocal of the impedance of the circuit is the sum of the reciprocal of resistance and reciprocal of reactance. The expression of the impedance of the parallel RL circuit can be represented as

Impedance of a Parallel RC Circuit

Here as the capacitor and resistor are connected in parallel, the reciprocal of the impedance of the circuit is the sum of the reciprocal of resistance and reciprocal of the reactance of the capacitor. Finally, we can write the expression of the impedance of the parallel RC circuit as

Impedance of a Series RLC Circuit

Here resistors, capacitors, and inductors are connected in series. The total reactance of the circuit is the sum of the reactance of inductors and capacitors. The reactance of the capacitors is taken as negative. The expression of impedance of a series RLC circuit is

Impedance of a Parallel RLC Circuit

Here resistor, capacitor, and inductor are connected in parallel. In the same way, the equivalent impedance of a parallel RLC circuit can be determined and the finally the expression of the impedance of a parallel RLC circuit is

Polar Representation of Impedance

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Electrical Impedance
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