Haryana PMT Haryana PMT Solved Paper-2011

  • question_answer An electric wire of area of cross-section a and    length \[l\] has resistance R. Another wire of same material and same length has cross-sectional            area 4a, then the resistance of another wire is

    A)                  4R                                         

    B) \[\frac{R}{4}\]

    C)                  \[\frac{R}{16}\]                                               

    D)  16R

    Correct Answer: B

    Solution :

                    Resistance, \[\text{R=}\,\rho \frac{\text{l}}{\text{A}}\]                 \[\therefore \] \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{l}_{1}}}{{{l}_{2}}}\times \frac{{{A}_{2}}}{{{A}_{1}}}\]                         \[\frac{{{R}_{{}}}}{{{R}_{2}}}=\frac{{{l}_{{}}}}{{{l}_{{}}}}\times \frac{{{4}_{a}}}{a}\]                         \[{{\text{R}}_{\text{2}}}\text{ }\!\!\times\!\!\text{ }\frac{\text{R}}{\text{4}}\]

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