A european outlet supplies 220 v (rms) at 50 hz. how many times per second is the magnitude of the voltage equal to 220 v

The amplitude of the sine wave with RMS value of 220 V is

A = 220√2 volts.

The sine waveform is

v (t) = 220√2 sin (2πft)

where

f = 50 Hz, the frequency.

The period is

T = 1/f = 1/50 = 0.02 s

Use a graphical solution (shown below) to determine the number of times that v (t) = 220 in the interval t = [0, 0.02] s.

There are 2 instances when the voltage is 220 V in the interval t = [0, 0.02] s.

Note that 1 second is an integral multiple of 0.02 seconds.

Therefore in the interval [0,1], the number of instances when v (t) = 220 V is

(1/0.02) * 2 = 100

Answer: 100