Series Two

How do i find the value of two resistors given their total resistance in parallel and series circuits?

Two resistors connected in series have an equivalent resistance of 658.2 Ω. When they are connected in parallel, their equivalent resistance is 157.3 Ω. Find the resistance of each resistor.

       Rs = Ra + Rь = 658.2  … (series)
           Rь = 658.2 − Ra  …  equation 1

      Rp = (Ra) • (Rь) ⁄ (Ra + Rь) = 157.3 … (parallel) … equation 2

  (Ra) • (658.2 − Ra) ⁄ (Ra + 658.2 − Ra) = 157.3 … substituted for Rь

    [ (658.2) (Ra) − (Ra)² ] ⁄ (658.2) = 157.3

          (658.2) (Ra) − (Ra)² = 103534.86

     (Ra)² − (658.2) (Ra) + 103534.86 = 0  …  quadratic

         ___________________
 Ra = [ 658.2 ± √(658.2)² − 4(103534.86) ]   ⁄   2

 Ra and Rь are 398.2 Ω and 260 Ω

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