In a certain circuit current changes with time accroding to `i=2sqrt(t)`. r.m.s. value of current between `t=2` to `t=4s` will be

Options

A. `3A`
B. `3sqrt(3)A`
C. `2sqrt(3)A`
D. `(2-sqrt(2))A`

Answer

C

Explanation

`bar(i^(2))=(inti^(2)dt)/(int dt)=(int_(2)^(4)(4t)dt)/(int_(2)^(4)dt)=(4int_(2)^(4)tdt)/2`
`=2[(t^(2))/2]_(2)^(4)=[t^(2)]_(2)^(4)=12`
`implies i_(rms)=sqrt(i^(2))=sqrt(12)=2sqrt(3)A`