1. Two wires – A and B – with circular cross-sections have identical lengths and are made of the same material. Yet, wire A has four times t

Question

1. Two wires – A and B – with circular cross-sections have identical lengths and are made of the same material. Yet, wire A has four times the resistance of wire B. How many times greater is the diameter of wire B than wire A?

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Neala 5 months 2021-08-05T00:53:01+00:00 1 Answers 105 views 0

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    2021-08-05T00:54:42+00:00

    Answer:

    Diameter of wire B is 2 times the diameter of wire A

    Explanation:

    We have given two wire A and B

    They are made up of same material and length of both the wire is sane

    So l_A=l_B

    Let the resistivity of both the wire is \rho

    It is given that wire A has 4 times the resistance as wire B

    So R_A=4R_B

    So \frac{\rho l_A}{a_A}=4\frac{\rho l_B}{a_B} ( As l_A=l_B )

    \frac{a_A}{a_B}=\frac{1}{4}

    \frac{d_A^2}{d_B^2}=\frac{1}{4}

    \frac{d_A}{d_B}=\frac{1}{2}

    d_B=2d_A

    So diameter of wire B is 2 times the diameter of wire A

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