Define the term impedance of a series LCR circuit. Derive a mathematical expression for it using phasor diagram.
Obtain resonance frequency of a series LCR circuit with L=2.0 H, C=32µF and R=10 Ω
The net resistance of an AC circuit elements (L,C,R) is together called impedance.
Suppose resistance R, inductance L and capacitance C are connected in series and an alternating source of voltage V =V0sinωt is applied across it. (fig. a) On account of being in series, the current (i ) flowing through all of them is the same.
Suppose the voltage across resistance R is VR, voltage across inductance L is VL and voltage across capacitance C is VC. The voltage VR and current i are in the same phase, the voltage VL will lead the current by angle 90° while the voltage VC will lag behind the current by angle 90° (fig. b). Clearly VC and VL are in opposite directions, therefore their resultant potential difference =VC -VL (if VC >VC ). Thus VR and (VC -VL ) are mutually perpendicular and the phase difference between them is 90°. As applied voltage across the circuit is V, the resultant of VR and (VC -VL ) will also be V. From fig.
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