A series circuit consists of an AC generator with an rms voltage of120 V at a fr

Question

A series circuit consists of an AC generator with an rms voltage of120 V at a frequency of 68.7 Hzand a magnetic buzzer with a resistance of 81 and an inductanceof 105 mH. A) Find the circuit's powerfactor. B) Then suppose a higherpower factor is desired. Can a power factor of 1.00 be achieved bychanging the inductance or any other circuitparameters? C) Show that a power factorof 1.00 can be attained by inserting a capacitor into the originalcircuit. D) Find the value of iscapacitance.
A) Find the circuit's powerfactor. B) Then suppose a higherpower factor is desired. Can a power factor of 1.00 be achieved bychanging the inductance or any other circuitparameters? C) Show that a power factorof 1.00 can be attained by inserting a capacitor into the originalcircuit. D) Find the value of iscapacitance.

Explanation / Answer

given Vrms = 120V frequency f = 68.7Hz resistance R = 81 inductance L = 105*10-3H a) the inductive reactance is XL = L                                              = L(2f) In LR circuit the phase angle is given as = tan-1(L/R)       = ---------- the power factor is given as cos b) powe factor can be closely achieved to one by decreasing thevalue of L or by increasing the value of R ,so that value decreases & hence cos value will be closer toone . But power factor of exactly one cannot be acheived by LRckt. power factor of exactly one can be achieved by introducing acapacitor in series with L&R. c) we have in series LCR ckt , the phase angle between current& applied emf as       =tan-1(L-1/C) /R    is zero when L = 1/C i.e thecurrent is in phase with the applied emf so that cos is one thus the power factor of one can be acheived we have     L = 1/C     or      XL = 1/XC    or     XL = 1/2fC    or      C = 1/XL*2f          =------------    or     XL = 1/2fC    or      C = 1/XL*2f          =------------    

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