The rms value of the saw-tooth voltage of peak value V₀ from t = 0 to t = 2T as shown in figure is given by

As, peak value of voltage, V₀

$\mathrm{V}\left(\mathrm{t}\right)=\frac{2{\mathrm{V}}_0}{\mathrm{T}}\mathrm{t}$

rms value of the saw-tooth voltage of peak value V₀

${\mathrm{V}}_{\mathrm{rms}}=\sqrt{<{\mathrm{V}}^2>}=\sqrt{\frac{{\displaystyle {\int }_{-\mathrm{T}/2}^{+\mathrm{T}/2}\frac{4{\mathrm{V}}_0^2}{{\mathrm{T}}^2}{\mathrm{t}}^2\mathrm{dt}}}{{\displaystyle {\int }_{-\mathrm{T}/2}^{+\mathrm{T}/2}\mathrm{dt}}}}=\sqrt{\frac{{\mathrm{V}}_0^2}{3}}=\frac{{\mathrm{V}}_0}{\sqrt{3}}$