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. `3 A`
B. `3 sqt3 A`
C. `2 sqt3 A`
D. `sqt3 A`

Answer

C

Explanation

As `i= 2 sqrt t`,at ` t = 2 s, i_(1) = 2 sqrt2`
and at `t = 4 s, i_(2) = 2 sqrt4 = 4`
`i_(rms) = sqrt((i_(1)^(2) + i_(2)^(2))/(2)) = sqrt(((2 sqrt2)^(2) + 4^(2))/(2))`
`= sqrt(12) = 2 sqrt(3) A`