AC Circuits

 

ALTERNATING CURRENT (Chapter 31)

KEY TERMS: alternating current, ac source, voltage amplitude, current amplitude, phasors, phasor diagram, phase angle, inductive reactance, capacitance reactance, root-mean-square (rms) current, power factor, resonance, resonant angular frequency, transformer.

 

 
Fig. 31.2 Phasors (Think of a phasor as a rotating vector.)
  

 

 

 

 

The phasors shown here are I and VR, the amplitude of the ac current through the resistor and the ac voltage across the resistor. The phasors are rotating at an angular speed of:
w radians per second.

(1 radian = 360 deg. / 2 p = 57.3 deg.)

Phasor diagrams are easier to draw than the sinusoidal curves, and are easier to use to calcite phase angles.
Fig. 31.7 The voltage across the resistor can be called the "resistance phasor"
 

 

 

 

 

 

 

The phasors shown here are I and VL, the amplitude of the ac current through the inductor and the ac voltage across the inductor. The phasors are rotating at an angular speed of:
w radians per second.
Fig. 31.8 The voltage across
the inductor can be called the
"inductance phasor"
  

 

 

 

 

 

 

The phasors shown here are I and VC, the amplitude of the ac current "through" the capacitor and the ac voltage across the capacitor. The phasors are rotating at an angular speed of:
w radians per second.
Fig. 31.9 The voltage across
the capacitor can be called
the "capacitance phasor"
  

 

 

 
Fig. 31.12 Crossover network in a loudspeaker
(the crossover frequency is determined by XL = XC)
  

 

 

 

 

Series RLC circuit.

 

 

In (a) XL > XC, and the driving voltage (V) leads the current by a phase angle of f. (Remember: ELI)

 

 

 

In (b) XL < XC, and the driving voltage (V) lags the current by a phase angle of f.
(Remember: ICE)
Fig. 31.13 Phasor diagrams
for RLC circuits
  

 

 

 

 

 
Fig. 31.15 Sinusoidal graphs for RLC circuit
(Phasor diagrams are better!)
  

 

 

 

 

 
Fig. 31.16 Power and other graphs for an RLC circuit
  

 

 

 

 

 

 
Fig. 31.17 Average power in ac circuit is 0.5 I V cos f
  

 

 

 

 

 
Hair dryer - average power delivered to the dryer is = Vrms^2 / R
  

 

 

 

 

 
Fig. 31.19 Current amplitude vs w for series RLC circuit with various R values.
  

 

 

 

 

 
Fig. 31.20 Radio tuning circuit at resonance.
(Note: VL = VC and are out of phase by 180 degrees at resonance)
  

 

 

 

 

 
Fig. 31.21 Step-up transformer: V2 / V1 = N2 / N1.
The flux change is the same in both the primary coil and secondary coil.
 

 

 

 

 

 
Very large transformer at a power station
  

 

 

 

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© 2009 J. F. Becker