Subsection 4.1.4 Sine Waves
Electrical systems may be described as either DC (direct current) or AC (alternating current) depending on the voltage supply.
In DC systems, the power supply maintains a constant polarity, i.e. one terminal is always positive, and the other is always negative, and the supply voltage is usually fairly steady. Batteries and solar cells are examples of DC voltage sources. In DC circuits, current always flows around the circuit in exactly one direction, from the positive to the negative terminal. Figure 4.1.3 is a simple example of a DC system. The current flows from the positive terminal of the battery, through the bulb, the switch, and then returns to the negative terminal of the battery.
On the other hand, in AC systems the polarity of the voltage switches periodically in a repeating pattern. This causes the current in the circuit to change periodically as well. In this section we discuss some important properties of period waves
Periodic Waves.
A periodic waveform is a quantity, (voltage, current, power, for example) that varies in a repeating pattern over time. Standard AC voltage takes the form of a sine wave as shown in Figure 4.1.5, although other shapes such as square waves and sawtooth waves are used in electronic circuits.
Periodic waveforms are characterized by several key properties that define its behavior and shape:
Amplitude (Peak value): The amplitude is the maximum value reached by the waveform during each cycle. It represents the highest positive or negative value from the reference level (usually zero volts).
Frequency The frequency \(f\) of a periodic waveform is the number of complete cycles or oscillations that occur in one second. It is measured in Hertz (Hz). Frequency determines how quickly the voltage waveform repeats itself. Standard electrical voltage in the United States is generated at 60 Hz, while 50 Hz is used in Europe and Japan.
Period The period \(T\) of a periodic wave is the time it takes for one complete cycle to occur. It is the reciprocal of frequency (\(T = 1 / f\)) and is measured in seconds.
Peak-to-Peak Value The peak-to-peak value is the difference between the maximum positive and maximum negative values in a waveform. It represents the total range of voltage variation.
Root Mean Square (RMS) Voltage The root mean square is a mathematical concept used to represent the effective or average value of a varying quantity, such as voltage or current, in an AC waveform. It provides a way to express the magnitude of an AC signal in a manner that is equivalent to the magnitude of a DC value.
RMS values, rather than peak or instantaneous values, are used to describe the properties of AC systems. For example, when you see the voltage rating on a household electrical device (e.g., 120V for North America), it’s the RMS value that’s being specified. Similarly, the current rating (e.g., 15A) refers to the RMS value of the current.
For a sinusoidal waveform (like the standard AC power supply waveform), the RMS value is approximately \(1/\sqrt{2} = 0.707\) times the peak value of the waveform.
\begin{equation*}
V_{\text{RMS}} = \frac{V_{\text{peak}}}{\sqrt{2}}\qquad V_{\text{peak}} =V_{\text{RMS}}\sqrt{2}
\end{equation*}
The RMS value of an AC voltage is the equivalent steady DC voltage that would produce the same amount of power dissipation across a resistor as the AC voltage across the same resistor. In other words, it’s the voltage that gives the same heating effect as the AC voltage. Similarly, the RMS value of an AC current is the equivalent steady DC current that would produce the same power dissipation in a resistor as the AC current through the same resistor.
Phase Shift Phase shift refers to the time difference between two periodic waveforms. It’s often expressed in degrees and indicates how far one waveform is shifted in time relative to another. A phase shift of 0 degrees means the waveforms are in sync, while a phase shift of 180 degrees means they are completely out of phase. Recall that capacitors and inductors cause a phase shift between current and voltage.
Three phase power.
Large AC generators including those on the training ship generate three phase power. Three phase power consists of three identical alternating voltage waveforms 120 degrees out of phase with each other, as shown in Figure 4.1.7.
Three-phase power is commonly used in industrial and commercial settings, as well as in larger residential complexes and power distribution networks. It’s well-suited for heavy machinery, motors, large-scale industrial processes, and high-power applications.
The three voltage sine waves can be separated and used individually to supply single phase power for homes, small businesses, and some light commercial applications. It’s suitable for powering lighting, appliances, and smaller electric loads.
