Physics for Scientists and Engineers 8ed - ch33 - PowerPoint Slides

# Physics for Scientists and Engineers 8ed - ch33 - PowerPoint Slides

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Chapter 33 Alternating Current Circuits

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AC Circuits An AC circuit consists of a combination of circuit elements and a power source The power source provides an alternative voltage, v Notation Note Lower case symbols will indicate instantaneous values Capital letters will indicate fixed values
AC Voltage The output of an AC power source is sinusoidal and varies with time according to the following equation: Δ v = Δ V max sin ω t Δ v is the instantaneous voltage Δ V max is the maximum output voltage of the source Also called the voltage amplitude ω is the angular frequency of the AC voltage

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AC Voltage, cont. The angular frequency is ƒ is the frequency of the source T is the period of the source The voltage is positive during one half of the cycle and negative during the other half 2 2 Ä T = =
AC Voltage, final The current in any circuit driven by an AC source is an alternating current that varies sinusoidally with time Commercial electric power plants in the US use a frequency of 60 Hz This corresponds with an angular frequency of 377 rad/s

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Resistors in an AC Circuit Consider a circuit consisting of an AC source and a resistor The AC source is symbolized by Δ v R = V max = V max sin ϖ t Δ v R is the instantaneous voltage across the resistor
Resistors in an AC Circuit, 2 The instantaneous current in the resistor is The instantaneous voltage across the resistor is also given as Δ v R = I max R sin ω t sin sin max max I R R v V i ¶ t ¶ t R R = = =

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Resistors in an AC Circuit, 3 The graph shows the current through and the voltage across the resistor The current and the voltage reach their maximum values at the same time The current and the voltage are said to be in phase
Active Figure 33.2 Adjust the resistance, frequency and V max Observe the results with the graph and the phasor diagram PLAY ACTIVE FIGURE

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Resistors in an AC Circuit, 4 For a sinusoidal applied voltage, the current in a resistor is always in phase with the voltage across the resistor The direction of the current has no effect on the behavior of the resistor Resistors behave essentially the same way in both DC and AC circuits
Phasor Diagram To simplify the analysis of AC circuits, a graphical constructor called a phasor diagram can be used A phasor is a vector whose length is proportional to the maximum value of the variable it represents

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Phasors, cont. The vector rotates counterclockwise at an angular speed equal to the angular frequency associated with the variable The projection of the phasor onto the vertical axis represents the instantaneous value of the quantity it represents
The average current in one cycle is zero The rms current is the average of importance in an AC circuit rms stands for root mean square Alternating voltages can also be discussed in terms of rms values 0 707 2 max rms max I I . I = = 0707 2 max max . rms

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Physics for Scientists and Engineers 8ed - ch33 - PowerPoint Slides

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