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20 March, 10:48

A wire with a resistance R is lengthened to 7.34 times its original length by pulling it through a small hole. Find the new resistance of the wire after it was stretched. Answer in units of R.

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  1. 20 March, 13:29
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    The resistance of a wire is given as

    R=ρl/A.

    So the first wire has resistance R and length l and resistivity ρ and area A.

    Now, the length of the wire is now stretched to 7.34 times it initial

    L2=7.34l

    Since the length ha increase by 7.34, the cross sectional area is reduced by 7.34

    Therefore, A2 = A/7.34

    The resistivity of the wire did not change

    Therefore

    Resistivity 1 is equal to resistivity 2

    ρ. = ρ

    R1A1/L1=R2A2/L2

    Since R=R, A1=A and L1 = l

    Also R2=?, A2 = A/7.34 and L2=7.34l

    RA/l=R2A/7.34l

    R2=RA/l*7.34l/A/7.34

    R2=7.34*7.34R

    R2=53.88R

    The new resistance is 53.88 times the old resistance
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