Capacitor Load The capacitive reactance of a capacitor

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Presentation transcript:

Capacitor Load The capacitive reactance of a capacitor Generalized Ohm’s law: Notice Ic and VC are amplitudes ICE

Inductive Load The Inductive reactance of a inductive Generalized Ohm’s law: Notice IL and VL are amplitudes ELI

The series RLC circuit 1. Same current through R, L, C Same frequency as in the source 2. Consider VR, VC, VL wt-f I e i VR vR VL VC vC

The series RLC circuit: Continuous Values at t. This relation has to be maintained as phosors are rotating General rules: KVL and KCL still hold, but values at the same t have to be used, i.e. vertical components in phasor diagram. Vectors operation for Amplitude v V

The series RLC circuit: Continuous =IZ =IR =I(XL-XC) Z is the impedance of the circuit

Examples =I(XL-XC) =IR =IZ 33-43P. A coil of inductance 88 mH and unknown resistance and a 0.94 mF are connected in series with an alternating emf of frequency 930 Hz. If the phase constant between the applied voltage and current is 75, what is the resistance of the coil. f=930 Hz wd=2pf

RLC Resonance =IZ =IR XL>XC: inductive loading =I(XL-XC) XL=XC: Resonance XC>XL: Capacitive loading

RLC Resonance: Cont

Conditions at Resonance =I(XL-XC) =IR =IZ I is a maximum Z is at minimum; Z=R; Z is purely resistive XL=XC; inductive reactance cancels capacitive reactance; net reactance is zero The phase angle is zero; the current is perfectly in phase with applied emf; the tangent of the phase angle is zero. The driven frequency is identical to the natural frequency. The power factor is unity