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Sum

Find the RMS value of the waveform given below:-

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#### Solution

The rms value of the alternating current is given by,

`"Irms"=sqrt(1/(t_2-t_1)int_(t_1)^(t_2)i^2(t)dt`

`t_1="T"` `t_2=2"T"` `i=I_msinthetat`

`"Irms"=sqrt(1/(2"T"-"T")int_"T"^(2"T")("I"_msinvarphit)^2("T")dt)="I"_msqrt(int_"T"^(2"T")sin^2thetatdt)="I"_msqrt([theta/2-(sin2theta)/4]_"T"^(2"T")`

`"Irms"="I"_msqrt[(2"T")/2-(sin4"T")/4-"T"/2+(sin2"T")/4]`

`"Irms"="I"_msqrt("T"/2-(sin4"T")/4+(sin2"T")/4)`

Concept: RMS and Average Value

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