JEE Main & Advanced Physics Current Electricity, Charging & Discharging Of Capacitors / वर्तमान बिजली, चार्ज और कैपेसिटर का निर Question Bank Electric Conduction Ohms and Resistance

  • 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 \[2d\] and length \[4L\] will be [CPMT 1984; MP PET 2002]

    A)                    \[2R\]

    B)                                      \[R\]

    C)                    \[R/2\]

    D)                                      \[R/4\]

    Correct Answer: B

    Solution :

                 \[R\propto \frac{l}{A}\propto \frac{l}{{{d}^{2}}}\] Þ \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{l}_{1}}}{{{l}_{2}}}\times \,{{\left( \frac{{{d}_{2}}}{{{d}_{1}}} \right)}^{2}}=\frac{L}{4L}\,{{\left( \frac{2d}{d} \right)}^{2}}=1\] Þ \[{{R}_{2}}={{R}_{1}}=R.\]


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