How to reduce alternating voltage with resistors

Electric power with alternating current

The tasks are not always so simple that one can only calculate the instantaneous values ​​using the angle function. Frequent is only the frequency (f) and the time (t) specified in order to determine the voltage or the current strength. The frequency indicates how often the current oscillates back and forth per second (number of periods per second), whereby each oscillation (period) corresponds to a 360 ° rotation in the unit circle. The unit for frequency is Hertz (Hz) and with normal AC voltages in households, the frequency is 50 Hz.

A 360 ° rotation in the unit circle corresponds to radians and that in turn corresponds to an arc length in the unit circle. This is the abbreviated form of 2 · π · r, since r is 1 in the unit circle and can therefore be omitted. If you have the value for the frequency, then you basically know how many revolutions that corresponds in the unit circle per second and that it will be Angular frequency (Symbol ω) called. Thus the angular frequency can be calculated with the formula ω = 2 · π · f be determined. The unit of measurement for the angular frequency is 1 / s or s-1. The angular frequency for normal AC voltages with 50 Hz is rounded up to 2 · π · 50 = 314.16 s-1.

A unique angular frequency can be assigned to each angle. This is because the angular frequency increases proportionally with the angle and the angle starts again at 0 ° after each full revolution (2 · π). At a frequency of 2, for example, the angle after 1 second is 360 ° and the angular frequency is 2 · π · 2 = 12.566 s-1 (2 full turns). At a frequency of 4, the angle after 1 second is also 360 ° and the angular frequency is 2 · π · 4 = 25.132 s-1 (4 full turns). Thus, one only needs to multiply the angular frequency (ω) by the duration (t) in order to determine the angle and from this in turn the instantaneous voltage or current strength. The following formulas can be derived from the relationships: