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

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

3. 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

4. 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

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

6. 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

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

8. RLC Resonance: Cont

9. 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