Sinusoidal alternating current  – Peak voltage and root mean square value of voltage

V(t) = V0  sin (2πft)        (set calculator to radians)

  • V         voltage in V
  • V0       peak voltage in V
  • f          frequency in Hz
  • t          time in s 

Vrms = ½ √2 V 0      

  • Vrms     root-mean-square value of voltage

            

Example 1                                                           

In the drawing above.                              

V 0 =10 V

T = 50 ms

 f = 1/T=1/(50 x 10-3) = 20 Hz

So :

V(t) = 10 sin (2π 20 t)

Vrms = ½ √2  V0 = ½ √2 ( 10) = 7.0 V

This means :

A  DC voltage of  7.0 V produced the same power as an AC voltage  with a peak voltage of

10.0 V

Example 2

The mains voltage is :  V =230 V  (This means :  V rms = 230 V)

Find the peak voltage.

Vrms = ½ √2  V 0

230 = ½ √2  V 0

V 0 = 325 V 

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