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Ratio of Resistors

  1. Mar 14, 2008 #1
    1. The problem statement, all variables and given/known data

    Two resistors of resistances R_1 and R_2, with R_2 > R_1, are connected to a voltage source with voltage V_0. When the resistors are connected in series, the current is I_s. When the resistors are connected in parallel, the current I_p from the source is equal to 10 I_s.

    Let r be the ratio R_1 / R_2. Find r.

    2. Relevant equations

    In series R = R1 + ... + RN
    In parallel 1 / R = 1 / R1 + ... + 1 / RN

    3. The attempt at a solution

    I_s (R_1 + R_2) = 10 I_s (R_1 * R_2) / (R_1 + R_2)

    0 = R_1^2 - 8 R_1 R_2 + R_2^2

    Quadraxtic equation R_1 = 4 +/- sqrt(9 - R_2)

    I don't know quite what to do now

    I need that ratio but it is just dirty

    (4 + sqrt(9 - R_2)) / R_2

    Help very much appreciated
     
  2. jcsd
  3. Mar 14, 2008 #2

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    Dividing by R2^2,

    r^2 - 8r + 1 = 0.

    Solve for r.
     
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