. A series circuit is connected to an a.c. source having voltage = . Using phasor diagram, derive expressions for impedance, instantaneous current and its phase relationship to the applied voltage. Also draw graphs of and versus for the circuit.
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12th
Physics
Alternating Current
LCR circuits
A series LCR circuit is con...
PHYSICS
A series LCR circuit is connected to an ac source having voltage V=V0sinωt. Derive the expression for the instantaneous current and its phase relationship to the applied voltage.
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Expression for Impedance in LCR series circuit: 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 V 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 > VL)
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 -V