Question

In `A.C` source peak value of `A.C` is the maximum value of current in either direction of the cycle. Root moon square `(RMS)` is also defined as the direct current which produces the same heating effect in a resistors as the actual `A.C`
Current time graph of different souce is given which one will have `R.M.S` value `V_(0)`
A.
B.
C.
D.

Answer 1

Correct Answer - A
(a) `V_("rms") = sqrt((2)/(T) int_(0)^(T//2) V^(2) dt)`
`V_("rms")^(2) = (2)/(T) int_(0)^(T//2) V_(0)^(2) dt = (2)/(T) V_(0)^(2) xx (T)/(2)`
`V_("rms") = V_(0)`
(b) `V_("rms") = sqrt((2)/(T) int_(0)^(T//2) V^(2) dt) = (2 V_(0))/(sqrt(3))`
(c ) `V_("rms") = (2 V_(0))/(sqrt(2)) = sqrt(2) V_(0)`
(d) `V_("rms") != V_(0)` so correct option is (a)