Part 2 – AC Sine Wave

AC Theory

Average or Mean Value

Direct current systems supply a constant voltage that does not vary with time.
When Voltage (V) is applied to a resistive load (R), the power (P) consumed is determined by the formula:

P = V2/R

chart DC voltage varying with time highlighting amplitude from 70 to -70 in increments of 10, time, average voltage= 15.1+25.5+3+53.4+68+62.3+35/7 =41.32 volts power = V2/R

Activity: Sinusoidal Voltage

Click the image hotspots to learn more about sinusoidal voltage.

Peak-to-Peak and RMS Values of AC Systems

Peak to Peak value

The magnitude of the voltage or current measured between the maximum positive value and the maximum negative value.

Peak to peak voltage chart highlighting peak voltage (Vp)
Peak to Peak Voltage

Root-Mean-Square Value (RMS Value)

The equivalent DC voltage that can deliver the same amount of energy to a resistor as the AC does over a cycle is defined as the root-mean-square of a sine wave.

The root-mean-square of a sine wave is:

    \Large \[ \frac{\text{Peak value}}{\sqrt{\frac{1}{2}}} \]

To determine the RMS value, three mathematical operations are carried out on the function representing the AC sine wave:

  1. The square of the wave is determined.
  2. The square of the wave from step 1 is averaged over time.
  3. The square root of the averaged square of the wave from step (2) is calculated.
RMS Value highlighting V=voltage, voltage squared =V2, Mean squared and root mean squared (RMS)
RMS Value

RMS value is necessary for measurement purposes because instantaneous values of alternating current and voltage constantly vary with time between positive and negative values. The average value of alternating current or voltage would be zero.

RMS Voltage

RMS voltage is calculated as follows:

Peak voltage x RMS value (0.707) = RMS voltage

i.e., For normal household voltage

  • 120 volts = peak voltage x 0.707
  • \frac{120}{0.707}  volts = peak voltage
  • 170 volts = peak voltage
RMS Values Graph highlighting 170 volts = peak value and 120 volts = RMS value
RMS Quantities

RMS quantities are measured by AC voltmeters and ammeters.

License

PEG-3722 Electrotechnology Copyright © by Josee Beaulieu. All Rights Reserved.

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