Find the rms and the average values of the saw tooth waveform shown in fig.
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Answer

`f(t)_(av)=0 ; f(t)_(rms)=sqrt((4)/(3))`

Explanation

Let us solve the question for time interval t=0 to t=1s. The rms and average value calcutaled for this time interval will be same for overall graph for a long time because the graph is repeating again and again.
Analytical Method: For `t=0 `to `t=1 s`
`f(t)=4t-2`
Average value:
`f(t)_(av) = (int_(0)^(1)f(t)dt)/(1-0) = (int_(0)^(1) (4t-2)dt)/(1) =[(4t^2)/(2)-2t[_(0)^(1)=0`
Hence, average value of wavefrom is zero.
`rms value=f(t)rms = sqrt( (int_(0)^(1)f(t)dt)/(1-0)) = sqrt( (int_(0)^(1) (4t-2)dt)/(1))`
`=sqrt([((4t-2)^(3))/(4xx3)]_(0)^(1)) =sqrt((4)/(3))`.