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## Fundamentals of AC circuits

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The DC (direct current) power supply provides a constant voltage and current, hence all resulting voltages and currents in DC circuit are constant and do not change with time. The polarity of DC voltage and direction of DC current do not change, only their magnitude changes. Before the nineteenth century, the DC power supply was the main form of electrical energy to provide electricity. An alternating voltage is called AC (alternating current) voltage and alternating current is called AC current. The AC voltage alternates its polarity and the AC current alternates its direction periodically. Since the AC power supply provides an alternating voltage and current, the resulting currents and voltages in AC circuit also periodically switch their polarities and directions. In the nineteenth century, DC and AC have had constant competition, AC gradually showed its advantages and rapidly developed in the latter of the nineteenth century, and is still commonly used in current industries, businesses, and homes throughout the world. This is because the AC power can be more cost-effective for long-distance transmission from power plants to industrial, commercial, or residential areas. This is why power transmission for electricity today is nearly all AC. It is also easy to convert from AC to DC, allowing for a wide range of applications.

Chapter Contents:

• 9.1 Introduction to alternating current (AC)
• 9.1.1 The difference between DC and AC
• 9.1.2 DC waveforms
• 9.1.3 AC waveforms
• 9.1.4 Period and frequency
• 9.1.5 The peak value and angular velocity of a sine function
• 9.1.6 The phase of a sine function
• 9.1.7 An example of a sine voltage
• 9.1.8 Phase difference of the sine function
• 9.1.9 An example of phase difference
• 9.2 Sinusoidal AC quantity
• 9.2.1 Peak value and peak–peak value
• 9.2.2 Average value
• 9.2.3 Instantaneous value
• 9.2.4 RMS (root-mean-square) value
• 9.2.5 Quantitative analysis of RMS value
• 9.2.6 RMS value of a periodical function
• 9.3 Phasors
• 9.3.1 Introduction to phasor notation
• 9.3.2 Complex numbers review
• 9.3.3 Phasor domain
• 9.3.4 Phasor diagram
• 9.3.5 Rotating factor
• 9.3.6 Differentiation and integration of the phasor
• 9.3.7 Examples of phasor domain
• 9.4 Resistors, capacitors, and inductors in sinusoidal AC circuits
• 9.4.1 Resistor's AC response
• 9.4.2 Resistor's AC response in time domain
• 9.4.3 Resistor's AC response in phasor domain
• 9.4.4 Inductor's AC response
• 9.4.5 The current and voltage in an inductive circuit
• 9.4.6 Characteristics of an inductor
• 9.4.7 Inductor's AC response in phasor domain
• 9.4.8 Capacitor's AC response
• 9.4.9 The current and voltage in a capacitive circuit
• 9.4.10 Characteristics of a capacitor
• 9.4.11 Capacitor's AC response in phasor domain
• Summary
• Practice problems

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