What is impedance ? Derive a relation for it in an a.c. series LCR-circuit. Show it by a vector diagram.

 

Dear student,

The impedance is the effective resistance of an electric circuit or component of alternating current arising from the combined effect of ohmic resistance and reactance.
The impedance Z of a series LCR circuit is the opposition of flow of current due to circuit resistance R,inductive reactance Xl and capacitive reactance Xc .If the inductive reactance is greater than capacitive reactance then the LCR circuit has a lagging phase angle.If the capacitive resistance is greater than inductive reactance then the circuit has a leading phase angle .
IF both are equal then circuit behaves as purely resistive circuit.
We know that,
Vs2=Vr2+Vl2-Vc2Where Vr=IRVl =IXl=jωLIVc =IXc=IjωC=-jIωCSubstituting the values Vs2=IR2+IXl2-IXc2Vs =IR2+Xl-Xc2Or the Impedance is Z=R2+Xl-Xc2

From the above impedance triangle, Using Pythagoras theorem,
tanϕ =Xl-XcRSinϕ =Xl-XcZCos ϕ =RZ
Regards.

,

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