Saved Bookmarks
| 1. |
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 tA. Determine the formula for the resultant current and also calculate the value of I_(rms). |
|
Answer» Solution :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 |
|