| The voltage time (V-t) graph for triangular wave having peak value \[{{V}_{0}}\] is as shown in figure. |
| The rms value of V in time interval from t=0 to T/4 is |
A) \[\frac{{{V}_{0}}}{\sqrt{3}}\]
B) \[\frac{{{V}_{0}}}{2}\]
C) \[\frac{{{V}_{0}}}{\sqrt{2}}\]
D) \[\frac{{{V}_{0}}}{3}\]
Correct Answer: A
Solution :
[a] \[V=\frac{{{V}_{0}}}{T/4}t\Rightarrow \,\,\,\,V=\frac{4{{V}_{0}}}{T}t\] \[\Rightarrow \,\,\,{{V}_{rms}}=\sqrt{<{{V}^{2}}>}=\frac{4{{V}_{0}}}{T}\sqrt{<t>}\] \[=\frac{4{{V}_{0}}}{T}\left\{ \frac{\int\limits_{0}^{T/4}{{{t}^{2}}dt}}{\int\limits_{0}^{T/4}{dt}} \right\}=\frac{{{V}_{0}}}{\sqrt{3}}\]
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