A) \[\frac{{{V}_{0}}}{\sqrt{3}}\]
B) \[{{V}_{0}}\]
C) \[\frac{{{V}_{0}}}{\sqrt{2}}\]
D) \[\frac{{{V}_{0}}}{2}\]
Correct Answer: C
Solution :
(c) \[\frac{{{V}_{0}}}{\sqrt{2}}\] \[V={{V}_{0}}\] for \[0\le t\le \frac{T}{2}\] \[V=0\] for \[\frac{T}{2}\le t\le T\] \[{{V}_{rms}}={{\left[ \frac{\int{_{0}^{T}{{V}^{2}}dt}}{\int{_{0}^{T}dt}} \right]}^{1/2}}={{\left[ \frac{\int{_{0}^{T/2}V_{0}^{2}dt+\int{_{T/2}^{T}(0)dt}}}{\int{_{0}^{T}dt}} \right]}^{1/2}}\] \[={{\left[ \frac{V_{0}^{2}}{T}[t]_{0}^{T/2} \right]}^{1/2}}={{\left[ \frac{V_{0}^{2}}{T}\left( \frac{T}{2} \right) \right]}^{1/2}}=\frac{{{V}_{0}}}{\sqrt{2}}\]
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