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24 November, 07:28

Two wires when connected in series have an equivalent resistance of 18ohm nd when in parallel an equivalent resistance of 4ohm find their resistance

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Answers (1)
  1. 24 November, 07:40
    0
    Givens

    r1 + r2 = 18

    r1*r2 / (r1 + r2) = 4

    Sub and Solve

    There are many ways to proceed. I like to find r1*r2 and that simplifies things.

    substitute 18 for r1 + r2

    r1*r2 / 18 = 4 multiply by 18

    r1 * r2 = 4 * 18

    r1 * r2 = 72

    Now you can set up a quadratic. Using r1 + r2 = 18, solve for r1

    r1 = 18 - r2

    Substitute into r1*r2 = 72

    r2 * (18 - r2) = 72 Remove the brackets.

    18r2 - (r2) ^2 = 72 Bring the left side over to the right side.

    0 = (r2) ^2 - 18r^2 + 72

    This factors

    (r2 - 12) (r2 - 6) = 0

    r2 - 12 = 0

    r2 = 12

    or

    r2 - 6 = 0

    r2 = 6

    r1*r2 = 72

    r1*12 = 72

    r1 = 72 / 12

    r1 = 6

    r1 = 12 when r2 = 6.

    Answers

    r1 = 12

    r2 = 6

    or

    r1 = 6

    r2 = 12
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