An unknown resistor R is connected to a 19.0 resistor, and the combination is at

Question

An unknown resistor R is connected to a 19.0 resistor, and the combination is attached to an ideal battery. Whenthe two resistors are combined in parallel, they consume 6.90 timesas much power as when they are combined in series. Determine thetwo possible values for R.
Enter the smaller possible value ofR.
Enter the larger possible value of R.

R1 = 19.0
Runknown = ?
Pparallel = 6.90Pseries

I'm guessing this is the only information you can get from what'sgiven, but are you supposed to do quadratic formula to get the twovalues? Will rate lifesaver!

Explanation / Answer

Power in parallel P = V ^2 / ( RR ' / ( R + R ')   ---( 1) Power in series P ' = V ^ 2 / ( R + R ')   -----( 2) Given P = 6.9 P ' from eq(1) and ( 2 ) , V ^ 2 / [ R R ' / ( R + R ' )] = 6.9 * V ^ 2 / ( R + R ' )                                        ( R + R ' ) / R R ' = 6.9 / ( R + R ' )                                       (R + R ' ) ^ 2 = 6.9 R R '              Given R ' = 10 ohm plug this we get ( R + 19 ) ^ 2 = 6.9* 19 *R                         R ^ 2 + 38 R + 361 = 131.1 R                        R ^ 2 - 93.1 R + 361 = 0         R = { 93.1±[ -93.1^2 -(4*1*361) ] } / 2 ( 1)            = { 93.1 ± 84.99 } / 2            = 89.04 ohm   ( or ) 4.055 ohm                                                                   

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