The r.m.s. voltage of the wave form shown is

Options

A. 10V
B. 7V
C. `6.37`V
D. None of these

Answer

A

Explanation

`V_(rms ) = sqrt((int_(t_(1))^(t_(2)) V^(2)dt)/(int_(t_(1))^(t_(2))dt))=sqrt((int _(0)^(T//2)(10)^(2)dt + int _(T//2) ^(T) (-10) ^(2)dt)/(int_(0)^(T)dt))`
`= sqrt((100 ((T)/(2))+100 [T-(T)/(2 )])/(T ))=sqrt((2xx100xx(T )/(2))/(T ))`
`=sqrt(100)=10V`