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KVPY Sample Paper KVPY Stream-SX Model Paper-27

  • question_answer
    Let V and I be the readings of the voltmeter and the ammeter respectively as shown in the figure. Let \[{{\operatorname{R}}_{v}}\], and \[{{\operatorname{R}}_{A}}\] be their corresponding resistance Therefore,

    A) \[R=\frac{V}{I}\]

    B) \[R=\frac{V}{I-\left( \frac{V}{{{R}_{V}}} \right)}\]

    C) \[R={{R}_{v}}-{{R}_{A}}\]     

    D) \[R=\frac{V\left( R+{{R}_{A}} \right)}{I{{R}_{A}}}\]

    Correct Answer: B

    Solution :

    \[\frac{R{{R}_{V}}}{R+{{R}_{V}}}.I=V\]
    \[\frac{R{{R}_{V}}}{R+{{R}_{V}}}=\frac{V}{I}\Rightarrow \frac{I}{V}=\frac{1}{R}+\frac{1}{{{R}_{V}}}\]\[\Rightarrow \]\[\frac{I}{V}-\frac{1}{{{R}_{V}}}=\frac{1}{R}\]\[\Rightarrow \]\[R=\frac{1}{\frac{1}{V}-\frac{1}{{{R}_{V}}}}=\frac{V}{I-\left( \frac{V}{{{R}_{V}}} \right)}\]


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