Alternating Current - Mathematics of AC Voltages

Mathematics of AC Voltages

Alternating currents are accompanied (or caused) by alternating voltages. An AC voltage v can be described mathematically as a function of time by the following equation:

,

where

  • is the peak voltage (unit: volt),
  • is the angular frequency (unit: radians per second)
    • The angular frequency is related to the physical frequency, (unit = hertz), which represents the number of cycles per second, by the equation .
  • is the time (unit: second).

The peak-to-peak value of an AC voltage is defined as the difference between its positive peak and its negative peak. Since the maximum value of is +1 and the minimum value is −1, an AC voltage swings between and . The peak-to-peak voltage, usually written as or, is therefore .

Read more about this topic:  Alternating Current

Other articles related to "mathematics of ac voltages, ac, voltage":

Alternating Current - Mathematics of AC Voltages - Example
... To illustrate these concepts, consider a 230 V AC mains supply used in many countries around the world ... To determine the peak voltage (amplitude), we can rearrange the above equation to For our 230 V AC, the peak voltage is therefore, which is about 325 V ... The peak-to-peak value of the 230 V AC is double that, at about 650 V ...

Famous quotes containing the words mathematics of and/or mathematics:

    Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.
    Walter Reisch (1903–1963)

    Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.
    Simone Weil (1909–1943)