Question

Derive an expression for the impedance of an a.c. circuit with series L.C.R Combination.

Answer 1

The impedance Z of a series LCR Circuit is defined as opposition to the flow of current due circuit resistance R, inductive reactance, XL and capacitive reactance, XC. If the inductive reactance is greater than the capacitive reactance i.e XL > XC, then the RLC circuit has lagging phase angle and if the capacitive reactance is greater than the inductive reactance i.e XC > XL then, the RLC circuit have leading phase angle and if both inductive and capacitive are same i.e XL = XC then circuit will behave as purely resistive circuit. We know that
Total voltage, voltage across resistance, voltage across capacitor and voltage across inductor are related in LCR ciruit as Vs2=VR2+(VL−VC)2Where,VR= IRVC= IXCVL= IXLSubstituiting these values Vs2=IR2+(IXL− IXC)2Vs2=I2[R2+(XL− XC)2]Vs2I2=[R2+(XL− XC)2]VsI=Z=[R2+(XL− XC)2]

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