A metal wire of resistance R is cut into five equal pieces that are then placed together side by side to form a new cable with a length equa

Question

A metal wire of resistance R is cut into five equal pieces that are then placed together side by side to form a new cable with a length equal to one-fifth the original length. What is the resistance of this new cable

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Farah 7 days 2021-07-22T21:58:53+00:00 1 Answers 5 views 0

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    2021-07-22T22:00:36+00:00

    Answer:

    R / 25

    Explanation:

    Let the initial length of the wire is L and its resistance is R.

    Now the length is cut into 5 equal parts.

    The resistance of a wire is directly proportional to the length of the wire, thus, the resistance of each portion of the wire is R/5.

    Now the five pieces are connected in parallel combination, the equivalent resistance is

    \frac{1}{R_{eq}}=\frac{5}{R}+\frac{5}{R}+\frac{5}{R}+\frac{5}{R}+\frac{5}{R}

    R_{eq}=\frac{R}{25}

    Thus, the resistance of the new cable is R / 25.

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