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An electric current has both A.C. and D....

An electric current has both A.C. and D.C. components . The value of D.C. component is equal to 12A while the A.C. component is given as 1 `= 9 sin omega t ` A. Determine the formula for the resultant current and also calculate the value of `I_(rms)`.

Text Solution

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At time t, resultant current `:`
`I = 12 + 9 sin omega t `
Now `I_(rms ) = sqrt( lt I^(2) gt ) = sqrt( lt ( 12 + 9 sin omega t)^(2))`
`:. I_(rms) = sqrt( lt 144 gt + 216 sin omega t + 81 sin^(2) omega t gt )` ....(1)
Here, the average is taken over a time interval equal to the periodic time.
`:. lt 144 gt = 144`
`:. 216 lt sin omega t gt = 0` and `81 lt sin^(2) omega t gt = 81 xx (1)/(2) = 40.5 `
Putting these values in equ. (1),
` :. I_(rms) = sqrt( 144 + 0 + 40.5 )`
`= sqrt( 184. 5 )`
= 13.583
`~~ 13.58` A
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