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10th Class Science Electricity and Circuits Question Bank Electricity

  • question_answer
    The ratios of wire A and wire B respectively are \[\frac{Length\,{{L}_{A}}}{Length\,{{L}_{B}}}=\frac{5}{18}\] and \[\frac{Diameter\,{{D}_{A}}}{Diameter\,{{D}_{B}}}=\frac{2}{3};\] \[\frac{\text{Resistivity}{{\rho }_{A}}}{\text{Resistivity}{{\rho }_{B}}}=\frac{4}{9}.\] What is the ratio of the resistance of wire A to the resistance of wire B?

    A) 5 : 8                                      

    B) 10 : 54                 

    C) 18 : 5                                    

    D) 54 : 10

    Correct Answer: A

    Solution :

    \[R=\rho \frac{L}{A},{{R}_{A}}:{{R}_{B}}\] \[(4\times 5)\div {{(2)}^{2}}:(9\times 18)\div {{(3)}^{2}}=\frac{20}{4}=5;\] \[\frac{72}{9}=8\] Hence, the resistance of wire A to the resistance of wire B = 5 : 8


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