Review on R, L, C and RLC in AC circuits - PowerPoint PPT Presentation

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Review on R, L, C and RLC in AC circuits

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An AC power source is a sinusoidal voltage source which is described as ... measured between the two values of ? for which pav has half its maximum value. ... – PowerPoint PPT presentation

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Title: Review on R, L, C and RLC in AC circuits


1
Review on R, L, C and RLC in AC circuits
  • An AC power source is a sinusoidal voltage source
    which is described as
  • We study the current i as a function of time when
    a resistor, inductor, capacitor or the serial
    connection of the three, to the AC voltage source.

When resistance is involved,
2
Assuming AC voltage source
3
Power discussion of RLC in an AC circuit
I did not discuss power with L or C in AC
circuit. Because there was no power consumed.
With R comes into the play, we have to examine
the power issue. The power delivered from the AC
voltage source is
The (more useful) average power is
The final result
4
Power and phase
The average power delivered from the AC voltage
source to the RLC circuit is
This power depends on the phase angle. Circuits
involving heavy motors (heavy inductive load)
usually have capacitors to shift the phase to
improve the power delivery efficiency.
5
Resonance in an AC Circuit
A series RLC circuit, R0.01O, L 4.34mH,
C1.00mF. ?Vmax150 V. Complete the following
table.
See the spreadsheet
Formula needed
6
Resonance in an AC Circuit
From these formulas
When
We have
Under this condition,
This frequency is called the resonant frequency
7
Power also resonates
The average power is
Now I want to express the power as a function of
the angular frequency
So when
the power reaches a maximum resonates.
PLAY ACTIVE FIGURE
8
How narrow (good) is the resonance the Q
(quality) factor
The sharpness of the resonance curve is usually
described by a dimensionless parameter known as
the quality factor, Q
?? is the half-power width width of the average
power curve, measured between the two values of ?
for which pav has half its maximum value.
Because R usually comes from the resistance of
the wire that is used to construct the inductor,
one tries to design the inductor in such a way
that it maximizes the L, and minimizes the R.
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