NEET Sample Paper NEET Sample Test Paper-14

  • question_answer 45) In the circuit the figure. When key \[{{K}_{1}}\]is closed, the ammeter reads\[{{I}_{0}}\]whether\[{{K}_{2}}\]is open or closed. But, when\[{{K}_{1}}\]is open, the ammeter reads\[{{I}_{0}}/2,\]when\[{{K}_{2}}\]is closed. Assuming that ammeter resistance is much less than \[{{R}_{2}},\]find the values of rand\[{{R}_{1}}\](in ohms)

    A)  100, 50                       

    B)  50, 100

    C)  0, 100             

    D)  0, 50

    Correct Answer: D

    Solution :

    When\[{{K}_{1}}\]is closed, the resistance\[{{R}_{1}}\]is ineffective, Applying kirchoff's voltage law with\[{{k}_{1}}\]closed and\[{{K}_{2}}\]open, while moving through \[{{k}_{1}},{{k}_{2}}\]and the battery, we get \[{{I}_{0}}{{R}_{2}}+{{I}_{0}}r-\varepsilon =0\Rightarrow {{I}_{0}}=\frac{\varepsilon }{{{R}_{2}}+r}\] Applying Kirchoff?s voltage law with both \[{{k}_{1}}\]and\[{{k}_{2}}\]closed, while moving through \[{{k}_{1}},{{k}_{2}}\] and the battery, we get \[{{I}_{0}}{{R}_{2}}+(2{{I}_{0}})r-\varepsilon =0\Rightarrow {{I}_{0}}=\frac{\varepsilon }{{{R}_{2}}+2r}\] Equating the values of \[{{I}_{0}},\]we get \[\frac{\varepsilon }{{{R}_{2}}+r}=\frac{\varepsilon }{{{R}_{2}}+2r}\Rightarrow r=0\] Applying Kirchoff's voltage law while moving through \[{{R}_{1}},{{k}_{2}}\]and the battery, with \[{{k}_{1}}\] open and\[{{k}_{2}}\]closed, we get \[{{I}_{0}}{{R}_{1}}+\frac{{{I}_{0}}}{2}{{R}_{2}}-\varepsilon +{{I}_{0}}r=0\Rightarrow {{I}_{0}}=\frac{\varepsilon }{{{R}_{1}}+\frac{{{R}_{2}}}{2}+r}\] \[\therefore \]    \[\frac{\varepsilon }{{{R}_{1}}+\frac{{{R}_{2}}}{2}+r}=\frac{\varepsilon }{{{R}_{2}}+r}\] \[\Rightarrow \]            \[\frac{1}{{{R}_{1}}+50}=\frac{1}{100}\Rightarrow {{R}_{1}}=50\Omega \] Hence, the correction option is [d].

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