Download the basic principle of the ac generator is a direct consequence

Slide 1
Fig 33-CO, p.1033
.. the basic principle of the ac generator is a direct consequence of Faraday’s law
of induction. When a conducting loop is rotated in a magnetic field at constant
angular frequency ω , a sinusoidal voltage (emf) is induced in the loop. This
instantaneous voltage Δv is
where ΔV max is the maximum output voltage of the ac generator, or the voltage
amplitude, the angular frequency is
where f is the frequency of the generator (the
voltage source) and T is the period.
Commercial electric power plants in the United
States use a frequency of 60 Hz, which
corresponds to an angular frequency of 377 rad/s.
The voltage supplied by an AC
source is sinusoidal with a period T.
Slide 2
Fig 33-1, p.1034
To simplify our analysis of circuits containing two or more elements, we use
graphical constructions called phasor diagrams.
In these constructions, alternating (sinusoidal) quantities, such as current and
voltage, are represented by rotating vectors called phasors.
The length of the phasor represents the amplitude (maximum value) of the
quantity, and the projection of the phasor onto the vertical axis represents the
instantaneous value of the quantity.
As we shall see, a phasor diagram greatly simplifies matters when we must
combine several sinusoidally varying currents or voltages that have different
phases.
Slide 3
At any instant, the algebraic sum of the voltages around a closed
loop in a circuit must be zero (Kirchhoff’s loop rule).
where ΔvR is the instantaneous voltage across the
resistor. Therefore, the instantaneous current in
the resistor is
the maximum current:
Slide 4
Fig 33-2, p.1035
Slide 5
Fig 33-3, p.1035
Plots of the instantaneous current iR
and instantaneous voltage vR across
a resistor as functions of time.
The current is in phase with the
voltage, which means that the current
is zero when the voltage is zero,
maximum
when
the
voltage
is
maximum, and minimum when the
voltage is minimum.
 At time t = T, one cycle of the timevarying voltage and current has been
completed.
Slide 6
Fig 33-3a, p.1035
Phasor diagram for the resistive circuit
showing that the current is in phase with
the voltage.
What is of importance in an ac circuit is an average value of current, referred to as the
rms current
Slide 7
Fig 33-3b, p.1035
(a) Graph of the current in a resistor as a function of time
(b) Graph of the current squared in a resistor as a function of time.
Notice that the gray shaded regions under the curve and above the dashed line
for I
2
max/2
have the same area as the gray shaded regions above the curve and
below the dashed line for I 2 max/2. Thus, the average value of i 2 is I 2max/2.
Slide 8
Fig 33-5, p.1037
The voltage output of a generator is given by Δv = (200 V)sin ωt. Find the rms
current in the circuit when this generator is connected to a 100 Ω- resistor.
Slide 9
is the self-induced instantaneous voltage across
the inductor.
Slide 10
Fig 33-6, p.1038
the inductive reactance
Slide 11
dI
V L    L
V max sin t
dt
V max

IL 
sin(t  )
L
2
Slide 12
Fig 33-7a, p.1039
Slide 13
Fig 33-7b, p.1039
In a purely inductive ac circuit, L = 25.0 mH and the rms voltage is 150 V.
Calculate the inductive reactance and rms current in the circuit if the
frequency is 60.0 Hz.
Slide 14
Slide 15
Slide 16
Slide 17
Fig 33-9, p.1041
Slide 18
Fig 33-10, p.1041
Slide 19
Fig 33-10a, p.1041
Slide 20
Fig 33-10b, p.1041
capacitive reactance:
Slide 21
Slide 22
Φ the phase angle between the
current and the applied voltage
 the current at all points in a series ac circuit has the same amplitude and
phase
Slide 23
Fig 33-13a, p.1044
Slide 24
Slide 25
Fig 33-13b, p.1044
Slide 26
Fig 33-14, p.1044
Slide 27
Fig 33-14a, p.1044
Slide 28
Fig 33-14b, p.1044
Slide 29
Fig 33-14c, p.1044
(a) Phasor diagram for the series RLC circuit The phasor  VR is in phase with the
current phasor Imax, the phasor  VL leads Imax by 90°, and the phasor VC lags
Imax by 90°. The total voltage  Vmax makes an Angle  with Imax. (b) Simplified
version of the phasor diagram shown in part (a)
Slide 30
Fig 33-15, p.1045
An impedance triangle for a series RLC circuit gives the relationship Z R2 + (XL
- XC)2
Slide 31
Fig 33-16, p.1045
Slide 32
Table 33-1, p.1046
Slide 33
the phase angle
Slide 34
Slide 35
Slide 36
Slide 37
Slide 38
Slide 39
Slide 40
No power losses are associated with pure capacitors and pure inductors in
an ac circuit
When the current begins to increase in one direction in an ac circuit,
charge begins to accumulate on the capacitor, and a voltage drop
appears across it. When this voltage drop reaches its maximum value,
the energy stored in the capacitor is
However, this energy storage is only momentary. The capacitor is
charged and discharged twice during each cycle: Charge is delivered to
the capacitor during two quarters of the cycle and is returned to the
voltage source during the remaining two quarters. Therefore, the
average power supplied by the source is zero. In other words, no
power losses occur in a capacitor in an ac circuit.
Slide 41
For the RLC circuit , we can express the instantaneous power P
The average power
the quantity cos φ is called the power factor
the maximum voltage drop across the resistor is given by
Slide 42
In words, the average power delivered by the generator is converted to
internal energy in the resistor, just as in the case of a dc circuit. No
power loss occurs in an ideal inductor or capacitor.
When the load is purely resistive, then φ= 0, cos φ= 1, and
Slide 43
Slide 44
A series RLC circuit is said to be in resonance when the current has
its maximum value. In general, the rms current can be written
Because the impedance depends on the frequency of the source, the
current in the RLC circuit also depends on the frequency. The frequency ω0
at which XL-XC=0 is called the resonance frequency of the circuit. To find ω0
, we use the condition XL = XC ,from which we obtain , ω0 L =1/ ω0 C or
Slide 45
(a) The rms current versus frequency for a series RLC circuit, for three
values of R. The current reaches its maximum value at the resonance
frequency
. (b) Average power delivered to the circuit versus
frequency for the series RLC circuit, for two values of R.
Slide 46
Fig 33-19, p.1050
Slide 47
Fig 33-19a, p.1050
Slide 48
Fig 33-19b, p.1050
Slide 49
Fig 33-20, p.1051
Slide 50
Fig 33-21, p.1052
Slide 51
Fig 33-22, p.1052
Slide 52
p.1053
Slide 53
Fig 33-23, p.1053
Slide 54
p.1053
Slide 55
Fig 33-24, p.1055
Slide 56
Fig 33-24a, p.1055
Slide 57
Fig 33-24b, p.1055
Slide 58
Fig 33-25, p.1055
Slide 59
Fig 33-25a, p.1055
Slide 60
Fig 33-25b, p.1055
Slide 61
Fig 33-26, p.1056
Slide 62
Fig 33-26a, p.1056
Slide 63
Fig 33-26b, p.1056
Slide 64
Fig Q33-2, p.1058
Slide 65
Fig Q33-22, p.1058
Slide 66
Fig P33-3, p.1059
Slide 67
Fig P33-6, p.1059
Slide 68
Fig P33-7, p.1059
Slide 69
Fig P33-25, p.1060
Slide 70
Fig P33-26, p.1060
Slide 71
Fig P33-30, p.1061
Slide 72
Fig P33-36, p.1061
Slide 73
Fig P33-47, p.1062
Slide 74
Fig P33-55, p.1062
Slide 75
Fig P33-56, p.1062
Slide 76
Fig P33-58, p.1063
Slide 77
Fig P33-61, p.1063
Slide 78
Fig P33-62, p.1063
Slide 79
Fig P33-64, p.1063
Slide 80
Fig P33-69, p.1064
Slide 81
Fig P33-69a, p.1035
Slide 82
Fig P33-69b, p.1035
Slide 83