A) \[\sqrt{V_{0}^{2}-\frac{V_{1}^{2}}{2}}\]
B) \[\sqrt{V_{0}^{2}+\frac{V_{1}^{2}}{2}}\]
C) \[V_{0}^{2}+\frac{V_{1}^{2}}{2}\]
D) \[\frac{V_{1}^{2}}{2}+V_{0}^{2}\]
Correct Answer: B
Solution :
\[V_{rms}^{2}=\frac{1}{T}\int_{\,0}^{\,T}{{{V}^{2}}dt=\frac{1}{T}\int_{\,0}^{\,T}{{{({{V}_{0}}+{{V}_{1}}\cos \omega t)}^{2}}dt}}\] \[=\frac{1}{T}\int_{\,0}^{\,T}{(V_{0}^{2}-2\,{{V}_{0}}{{V}_{1}}\cos \omega t+V_{1}^{2}{{\cos }^{2}}\omega t)dt}\] \[=V_{0}^{2}+0+\frac{V_{1}^{2}}{2}\] \[\therefore {{V}_{rms}}=\sqrt{V_{0}^{2}+\frac{V_{1}^{2}}{2}}\]
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