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BHU PMT BHU PMT (Mains) Solved Paper-2009

  • question_answer
    The given four terminal network is part of a larger circuit. The points A, B, C are at the same potential. The potential difference between any one of A, B or C and D is 40 V. The potential difference between A and O is

    A)  10V                                      

    B)  15V

    C)  18V                                      

    D)  20V

    Correct Answer: A

    Solution :

                     According to Kirchhoff?s junction law     \[{{I}_{CO}}+{{I}_{OB}}+{{I}_{AO}}={{I}_{OD}}\]                 \[\Rightarrow \]\[\frac{{{V}_{C}}-{{V}_{O}}}{R}+\frac{{{V}_{B}}-{{V}_{O}}}{R}+\frac{{{V}_{A}}-{{V}_{O}}}{R}=\frac{{{V}_{O}}-{{V}_{D}}}{R}\]                 \[\Rightarrow \]\[3\left( \frac{{{V}_{A}}-{{V}_{O}}}{R} \right)=\frac{{{V}_{O}}-{{V}_{A}}+{{V}_{A}}-{{V}_{D}}}{R}\]                 \[\Rightarrow \]\[3\left[ \frac{{{V}_{A}}-{{V}_{O}}}{R} \right]=-\left[ \frac{{{V}_{A}}-{{V}_{O}}}{R} \right]+\left[ \frac{{{V}_{A}}-{{V}_{D}}}{R} \right]\]                 \[\Rightarrow \]\[4\left[ \frac{{{V}_{A}}-{{V}_{O}}}{R} \right]=\frac{{{V}_{A}}-{{V}_{D}}}{R}\]                 \[\Rightarrow \]\[4({{V}_{A}}-{{V}_{O}})=40\]                 \[\Rightarrow \]\[{{V}_{A}}-{{V}_{O}}=10V\]


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