An electric current has both D.C. and A.C. components D.C. component of 8A and A.C. component is given as `I=6sin omegat A`. So `l_(rms)` value of resultant current is .....

Options

A. 8.05 A
B. 9.05 A
C. 11.58 A
D. 13.58 A

Answer

B

Explanation

Resultant current at time t
`I=8+6 sin omegat`
`therefore I_(rms)=sqrt(ltI^2gt)=sqrt(lt(8+6 sin omegat)^2gt)`
`=sqrt(lt64gt + lt 96 sin omegatgt+lt 36 sin^2 omegatgt)`
But on one period `lt64gt`=64
`lt96sinomegatgt`=0
`lt36sin^2omegatgt=36xx1/2=18`
`therefore I_(rms)=sqrt(64+0+18)`
`=sqrt82`
= 9.05 A