Question

Calculate the rms value.

Answer 1

(√6)/3 ≈ 0.8165

Step-by-step explanation:

The RMS value is the square root of the mean of the square of the waveform over one period. It will be ...

`\displaystyle\sqrt{(1)/(T)\left(\int_{(T)/(4)}^{(3T)/(4)}{1^2}\,dt+\int_{(3t)/(4)}^{(5t)/(4)}{((-4)/(T)}(t-T))^2\,dt\right)}=\sqrt{(1)/(T)\left((T)/(2)+\left.(16)/(T^2)\cdot(1)/(3)(t-T)^3\right|_{(3t)/(4)}^{(5t)/(4)}\right)}\\\\=\sqrt{(1)/(T)\left((T)/(2)+(T)/(6)\right)}=\sqrt{(2)/(3)}=\boxed{(√(6))/(3)\approx0.8165}`