
ALTERNATING CURRENT (Chapter 31)
KEY
TERMS: alternating current, ac source, voltage amplitude, current amplitude,
phasors, phasor diagram, phase angle, inductive reactance, capacitance
reactance, rootmeansquare (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 Stepup 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


© 2009 J. F. Becker


