The voltage supplied to a circuit is given by `V=V_(0)t^(3/2)`, where t is time in second. Find the rms value of voltage for the period, t=0 to t=1s.

Explanation

Mean square voltage for an interval of time 0 to t can be written as follows :
` bar(V^(2)) = (1)/(t_(0)) int_(0)^(t) V^(2) dt `
`rArr " " bar(V^(2)) = (1)/(t_(0)) int_(0)^(t) V_(0)^(2)t^(3) dt `
`rArr " " bar(V^(2)) = (V_(0)^(2))/(t) [ (t^(4))/(4) ]_(0)^(t)`
`rArr " " bar(V^(2)) = (V_(0)^(2)t^(3))/(4)`
at t = 1
`rArr " " bar(V^(2)) = (V_(0)^(2))/(4)`
Root mean square voltage can be written as follows :
`V_(rms) = sqrt(bar(V^(2))) = (V_(0))/(2)`