Question

if the effective value of the sinusoidal voltage is 111 volts. its average value is
a. 100 V
b. 123.21 V
c. 156.51 V
d. 78.48 V​

Answer 1

Given :  effective value of the sinusoidal voltage is 111 volts

To Find : average value

a. 100 V

b. 123.21 V

c. 156.51 V

d. 78.48 V​

Solution:

The effective value of a sine also known as the Root Mean Squared  RMS value

RMS value is  the square root of the mean (average) of the square of the voltage or current.

effective value of the sinusoidal voltage is 111 volts.

=> RMS value is  111  Volt

Average Value of complete sinusoidal cycle is zero

but we consider it  for  half cycle

average value  = (1/π) ∫Vsint .dt

= (1/π) V (-cost)  + c

t = 0 to π

=  (1/π) V (-cost)  + c

= 2V/π

RMS Value  =  √(1/π) ∫V²sin²t .dt  

= √(1/π) ∫V²(1- Cos2t)/2 .dt  

= √(1/π) (V²(t/2- Sin2t /4)).dt  

= √(1/π)  V²(π/2) .dt

= √ V²/2

= V/√2

= 0.707V

RMS Value   = effective value = 111V

=> 0.707V  = 111

=> V = 157 V

average value  =    2V/π

=  2(157)/π

= 314/3.14

= 100V

Direct formula :

Vrms = 1.11  * Vaverage  for sinusoidal

if the effective value of the sinusoidal voltage is 111 volts. its average value is  . 100 V

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Answer 2

Answer:

average value is 100 volt