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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
Fig 33-19, p.1050
Slide 41
Fig 33-19a, p.1050
Slide 42
Fig 33-19b, p.1050
Slide 43
Fig 33-20, p.1051
Slide 44
Fig 33-21, p.1052
Slide 45
Fig 33-22, p.1052
Slide 46
p.1053
Slide 47
Fig 33-23, p.1053
Slide 48
p.1053
Slide 49
Fig 33-24, p.1055
Slide 50
Fig 33-24a, p.1055
Slide 51
Fig 33-24b, p.1055
Slide 52
Fig 33-25, p.1055
Slide 53
Fig 33-25a, p.1055
Slide 54
Fig 33-25b, p.1055
Slide 55
Fig 33-26, p.1056
Slide 56
Fig 33-26a, p.1056
Slide 57
Fig 33-26b, p.1056
Slide 58
Fig Q33-2, p.1058
Slide 59
Fig Q33-22, p.1058
Slide 60
Fig P33-3, p.1059
Slide 61
Fig P33-6, p.1059
Slide 62
Fig P33-7, p.1059
Slide 63
Fig P33-25, p.1060
Slide 64
Fig P33-26, p.1060
Slide 65
Fig P33-30, p.1061
Slide 66
Fig P33-36, p.1061
Slide 67
Fig P33-47, p.1062
Slide 68
Fig P33-55, p.1062
Slide 69
Fig P33-56, p.1062
Slide 70
Fig P33-58, p.1063
Slide 71
Fig P33-61, p.1063
Slide 72
Fig P33-62, p.1063
Slide 73
Fig P33-64, p.1063
Slide 74
Fig P33-69, p.1064
Slide 75
Fig P33-69a, p.1035
Slide 76
Fig P33-69b, p.1035