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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 15

  • question_answer
    Three resistors are connected in series across a \[12\text{ }V\]battery. The first resistor has a value \[1\Omega \] second resistor has a voltage drop of \[4V\] and the third has a power dissipation of 12 W. Possible value of circuit current is

    A) \[4\,A\] or \[6\,A\]                      

    B) \[2\,A\] or \[4\,A\]  

    C) \[4\,A\]or \[8\,A\]         

    D) \[2\,A\]or \[6\,A\]

    Correct Answer: D

    Solution :

    [d] Let the unknown resistors are \[{{R}_{2}}\] and \[{{R}_{3}}\]. \[{{i}^{2}}{{R}_{3}}=12;\] \[i{{R}_{2}}=4\] \[{{\left[ \frac{4}{{{R}_{2}}} \right]}^{2}}{{R}_{3}}=12;\] \[\frac{16}{R_{2}^{2}}\times {{R}_{3}}=12;\] \[{{R}_{3}}=\frac{3}{4}R_{2}^{2}\] \[I(I+{{R}_{2}}+{{R}_{3}})=12\] \[\Rightarrow \,\,\,\,\frac{4}{{{R}_{2}}}\left( 1+{{R}_{2}}+\frac{3}{4}R_{2}^{2} \right)=12\] \[\Rightarrow \,\,\,\,3R_{2}^{2}-8{{R}_{2}}+4=0\] \[\Rightarrow \,\,\,\,{{R}_{2}}=2\Omega \]  or  \[\frac{2}{3}\Omega \] \[I=2A\] or  \[6A\]


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