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10th Class Science Electricity and Circuits Question Bank Electricity

  • question_answer
    The resistance of a wire of uniform diameter D and length L is R. The resistance of another wire of the same material but diameter 2 D and length 4 L will be

    A)  \[2R\]                 

    B)         \[R,\]  

    C)  \[\frac{R}{2}\]                 

    D)         \[\frac{R}{4}\]

    Correct Answer: B

    Solution :

     First we must write the formula of resistance in terms of diameter and length                 \[R=\frac{\rho L}{A}\propto \frac{L}{{{D}^{2}}}\] Now,     \[\frac{{{R}_{2}}}{{{R}_{1}}}=\frac{{{L}_{2}}/{{L}_{1}}}{{{({{D}_{2}}/{{D}_{1}})}^{2}}}=\frac{4}{{{2}^{2}}}=1\]


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