Find the rms and average value of the wavefrom shown in figure

Options

A. 8.5,10
B. 10.3,20
C. 15.2,15
D. 26,5

Answer

C

Explanation

The slope of the curve `AB` is `BC//AC = 20//T`. Next consider the function `y` at time `t` It is seen that `DE//AE = BC //AC = 10//T`
or `(y - 10)//t = 10 T` or `y = 10 + (10 //T) t`
This giveus the equation for the function of one cycle.
`Y_(av) = (1)/(T) int_(0)^(T) y dt = (1)/(T) int_(0)^(T) (10 + (10)/(T) t) dt`
`(1)/(T) int_(0)^(T) [10. dt + (10)/(T). t. dt] = (1)/(T) |10t + (5t^(2))/(T)|_(0)^(T) = 15`
Mean square value
`= (1)/(T) int_(0)^(T) y^(2) dt = int_(0)^(T) (10 + (10)/(T) t)^(2) dt`
` = (1)/(T) int_(0)^(T) (100 + (100)/(T^(2)) t^(2) + (200)/(T).t) dt`
`= (1)/(T) |100 t + (100 t^(3))/(3 T^(2)) + (100 t^(2))/(T) |_(0)^(T) = (700)/(3)`
or rms value `= 10 sqrt(7//3) = 15.2`