JEE Main & Advanced Sample Paper JEE Main - Mock Test - 37

  • question_answer
    The voltage time \[\left( V-t \right)\] graph for triangular wave having peak value \[{{V}_{0}}\] is as shown in figure. The rms value of V in time interval from \[t\text{ }=\text{ }0\] to T/4 is \[\frac{{{V}_{0}}}{\sqrt{x}}\] then find the value of x.  

    A) 5                     

    B)        4

    C) 7                     

    D)        3

    Correct Answer: C

    Solution :

    \[V=\frac{{{V}_{0}}}{T/4}t\,\,\,\,\,\,\,\,\Rightarrow \,\,\,V=\frac{4{{V}_{0}}}{T}t\] \[\Rightarrow \,\,\,{{V}_{rms}}=\sqrt{<{{V}^{2}}>}=\frac{4{{V}_{0}}}{T}\sqrt{<{{t}^{2}}>}=\,\,\frac{4{{V}_{0}}}{T}\left\{ \frac{\int\limits_{0}^{T/4}{{{t}^{2}}dt}}{\int\limits_{0}^{T/4}{dt}} \right\}\,\,=\,\,\frac{{{V}_{0}}}{\sqrt{3}}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner