Aeuropean 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

  100

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