7. Alternating current — Physics STD 12 Science — Question

$V=0$ for $\frac{T}{2} \leq t \leq T$

${V_{rms}} = \left[ {\frac{{\int\limits_0^T {{V^2}\,dt} }}{{\int\limits_0^T {dt} }}} \right] = {\left[ {\frac{{\int\limits_0^{T/2} {V_0^2\,dt}  + \int\limits_{T/2}^T {(0)\,dt} }}{{\int\limits_0^T {dt} }}} \right]^{1/2}}$

$ = {\left[ {\frac{{V_0^2}}{T}[t]_0^{T/2}} \right]^{1/2}}$

$ = {\left[ {\frac{{V_0^2}}{T}\left( {\frac{T}{2}} \right)} \right]^{1/2}}$

$ = {\left[ {\frac{{V_0^2}}{2}} \right]^{1/2}}$

${V_{rms}} = \frac{{{V_0}}}{{\sqrt 2 }}$