An alternating voltage is represented by the equation V=220 sin(400 πt × 57,3)v. Calculate
a) The range value of this voltage
b) The rms value of this voltage
c) The form factor
a) The range value of an alternating voltage is equal to the difference between its maximum value and its minimum value. In this case, the maximum value of the voltage is 220 volts, and the minimum value is -220 volts (since the sine function oscillates between 1 and -1). Therefore, the range value is:
Range = 220 - (-220) = 440 volts
b) The rms (root mean square) value of an alternating voltage is calculated by taking the square root of the mean of the squares of its instantaneous values over one complete cycle. The instantaneous value is given by the equation V = 220 sin(400 πt × 57,3), so we need to find the mean of the squares of this equation over one complete cycle.
The mean of the squares of a sine function over one complete cycle is 1/2, so the rms value of the voltage is:
rms value = √(1/2) * 220 = 155.56 volts (rounded to two decimal places)
c) The form factor of an alternating voltage is equal to the ratio of its rms value to its average (or mean) value. The average value of a sine function over one complete cycle is 0, so the form factor of this voltage is:
Form factor = rms value / average value = 155.56 / 0 = undefined