slide 1fig 33-co, p.1033. slide 2fig 33-1, p.1034.. the basic principle of the ac generator is a...
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Slide 1 Fig 33-CO, p.1033
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Slide 2 Fig 33-1, p.1034
.. 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 voltageamplitude, the angular frequency is
The voltage supplied by an AC source is sinusoidal with a period T.
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.
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Slide 3
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.
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Slide 4 Fig 33-2, p.1035
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:
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Slide 5 Fig 33-3, p.1035
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Slide 6 Fig 33-3a, 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 time-
varying voltage and current has been
completed.
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Slide 7 Fig 33-3b, 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
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Slide 8 Fig 33-5, p.1037
(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 2max/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.
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Slide 9
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.
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Slide 10 Fig 33-6, p.1038
is the self-induced instantaneous voltage across the inductor.
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Slide 11
the inductive reactance
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Slide 12 Fig 33-7a, p.1039
max
max
sin
sin( )2
L
L
dIV L V t
dtV
I tL
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Slide 13 Fig 33-7b, p.1039
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Slide 14
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.
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Slide 15
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Slide 16
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Slide 17 Fig 33-9, p.1041
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Slide 18 Fig 33-10, p.1041
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Slide 19 Fig 33-10a, p.1041
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Slide 20 Fig 33-10b, p.1041
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Slide 21
capacitive reactance:
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Slide 22
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Slide 23 Fig 33-13a, p.1044
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
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Slide 24
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Slide 25 Fig 33-13b, p.1044
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Slide 26 Fig 33-14, p.1044
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Slide 27 Fig 33-14a, p.1044
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Slide 28 Fig 33-14b, p.1044
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Slide 29 Fig 33-14c, p.1044
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Slide 30 Fig 33-15, p.1045
(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)
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Slide 31 Fig 33-16, p.1045
An impedance triangle for a series RLC circuit gives the relationship Z R2 + (XL - XC)2
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Slide 32 Table 33-1, p.1046
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Slide 33
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Slide 34
the phase angle
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Slide 35
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Slide 36
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Slide 37
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Slide 38
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Slide 39
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Slide 40 Fig 33-19, p.1050
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Slide 41 Fig 33-19a, p.1050
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Slide 42 Fig 33-19b, p.1050
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Slide 43 Fig 33-20, p.1051
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Slide 44 Fig 33-21, p.1052
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Slide 45 Fig 33-22, p.1052
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Slide 46 p.1053
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Slide 47 Fig 33-23, p.1053
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Slide 48 p.1053
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Slide 49 Fig 33-24, p.1055
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Slide 50 Fig 33-24a, p.1055
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Slide 51 Fig 33-24b, p.1055
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Slide 52 Fig 33-25, p.1055
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Slide 53 Fig 33-25a, p.1055
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Slide 54 Fig 33-25b, p.1055
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Slide 55 Fig 33-26, p.1056
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Slide 56 Fig 33-26a, p.1056
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Slide 57 Fig 33-26b, p.1056
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Slide 58 Fig Q33-2, p.1058
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Slide 59 Fig Q33-22, p.1058
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Slide 60 Fig P33-3, p.1059
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Slide 61 Fig P33-6, p.1059
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Slide 62 Fig P33-7, p.1059
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Slide 63 Fig P33-25, p.1060
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Slide 64 Fig P33-26, p.1060
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Slide 65 Fig P33-30, p.1061
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Slide 66 Fig P33-36, p.1061
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Slide 67 Fig P33-47, p.1062
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Slide 68 Fig P33-55, p.1062
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Slide 69 Fig P33-56, p.1062
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Slide 70 Fig P33-58, p.1063
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Slide 71 Fig P33-61, p.1063
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Slide 72 Fig P33-62, p.1063
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Slide 73 Fig P33-64, p.1063
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Slide 74 Fig P33-69, p.1064
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Slide 75 Fig P33-69a, p.1035
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Slide 76 Fig P33-69b, p.1035