Tru Physics

Chapter 25: Alternating Current

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25.1 Introduction

In this chapter, we will explore alternating current (AC), the type of electrical current that changes direction periodically. AC is the dominant form of electricity transmission and distribution for various applications, including power distribution to homes and industries.

25.2 AC Voltage and Current

An alternating voltage or current has a sinusoidal waveform that oscillates between positive and negative values. The key parameters for describing an AC waveform are amplitude, frequency, and phase.

25.2.1 Amplitude

The amplitude of an AC waveform is the maximum value of the voltage or current. In the case of voltage, the amplitude is called the peak voltage (V_p), and for current, it is the peak current (I_p).

25.2.2 Frequency

The frequency (f) of an AC waveform represents the number of complete oscillations or cycles that occur in one second. Frequency is measured in hertz (Hz).

25.2.3 Phase

The phase of an AC waveform indicates the position of the waveform in its cycle at a specific time. Phase is measured in degrees or radians, and it is essential for analyzing the relationship between voltage and current in AC circuits.

25.3 Root Mean Square (RMS) Values

The root mean square (RMS) value is a measure of the effective value of an AC voltage or current, which is the value that delivers the same power to a resistive load as a direct current (DC) voltage or current of the same value. The RMS values for voltage (V_{RMS}) and current (I_{RMS}) are given by the following equations:

V_{RMS} = \dfrac{V_p }{\sqrt{2}}

I_{RMS} = \dfrac{I_p }{\sqrt{2}}

25.4 AC Circuit Analysis

AC circuit analysis involves finding the voltage, current, and power in circuits containing resistors, inductors, capacitors, and AC voltage sources. To analyze AC circuits, we need to consider impedance, phasor representation, and complex power.

25.4.1 Impedance

Impedance (Z) is a complex quantity that describes how a circuit element resists the flow of AC current. It is defined as the ratio of the phasor voltage to the phasor current. The impedance of a resistor, inductor, and capacitor are given by the following equations:

Z_R = R

Z_L = j\omega L

Z_C = \dfrac{1}{j\omega C}

where j is the imaginary unit. Generally, the convention is to use j instead of i in electrical engineering so as not to confuse it with current.

25.4.2 Phasor Representation

Phasors are complex numbers that represent the amplitude and phase of sinusoidal waveforms. Phasor representation simplifies AC circuit analysis by converting differential equations into algebraic equations.

25.4.3 Complex Power

Complex power (S) is a measure of the power in an AC circuit, considering both the real power (P) and reactive power (Q). It is given by the following equation:

S = P + jQ

where P represents the power dissipated as heat in resistive elements, and Q represents the power stored and released by inductive and capacitive elements.

25.5 Power Factor

The power factor (PF) is a dimensionless quantity that represents the ratio of the real power (P) to the apparent power (S) in an AC circuit. It is given by the following equation:

PF = \dfrac{P}{|S|}

A power factor close to 1 indicates that the circuit is mostly resistive, while a power factor close to 0 indicates a highly reactive circuit.

Chapter Summary

In this chapter, we explored alternating current (AC), its key parameters (amplitude, frequency, and phase), and the root mean square (RMS) values. We discussed AC circuit analysis, including impedance, phasor representation, and complex power calculations. Furthermore, we examined the behavior of resistors, capacitors, and inductors in AC circuits and their respective phase relationships between voltage and current. Understanding alternating current is crucial for numerous applications in power generation, distribution, and consumption, as it forms the basis of our modern power infrastructure. A solid foundation in AC circuit analysis will enable you to tackle more advanced topics in electrical engineering, such as transformers, transmission lines, and power systems, further deepening your knowledge and skills in this critical domain.

Continue to Chapter 26: Electromagnetic Waves

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