Figure shows one cycle of an alternating current with the segments AB, BC, CD, DE being symmetrical and parabolic. The root mean square value of this current over one cycle is x mA, find x.

Options

A. 1 mA
B. 2 mA
C. 3 mA
D. 4 mA

Answer

A

Explanation

RMS value over one cycle = RMS value over AB.
`0 le t le 15`
`i(t) = sqrt5t^(2)c " i_(rms) = sqrt(lt i^(2) gt) = sqrt((5int_(0)^(1) t^(4)dt)/(int_(0)^(1) dt)) = 1 mA`