The rms value of potential difference `V` shown in the figure is

Options

A. `(V_(0))/(sqrt(3))`
B. `V_(0)`
C. `(V_(0))/(sqrt(2))`
D. `(V_(0))/(2)`

Answer

C

Explanation

`V=V_(0)` for `0 le t le (T)/(2)`
V = 0 for `(T)/(2)le t le T`
`V_("rms")=[(int_(0)^(T)V^(2)dt)/(int_(0)^(T)dt)]^(1//2)=[(int_(0)^(T//2)V_(0)^(2)dt+int_(T//2)^(T)(0)dt)/(int_(0)^(T)dt)]^(1//2)`
`=[(V_(0)^(2))/(T)[t]_(0)^(T//2)]^(1//2)=[(V_(0)^(2))/(T)((T)/(2))]^(1//2)=(V_(0))/(sqrt(2))`