Question

An unknown resistor R is connected to a 11.0 Ω resistor, and the combination is attached to an ideal battery. When the two resistors are combined in parallel, they consume 6.60 times as much power as when they are combined in series. Determine the two possible values for R.

Answer 1

case 1) in series

Req = R+11 , battery = V volts

power consumed P1 = V^2/(R+11)

case 2) in parallel

Req = R*11/(R+11)

power consumed P2 = V^2*(R+11)/(11*R)

=> as given P2 = 6.60*P1

=> V^2*(R+11)/(11*R) = 6.60*V^2/(R+11)

=> (R+11)^2 = 6.60*11R

=> R^2 + 22R + 121 = 72.6R

=> R^2 - 50.6R + 121 = 0

=> R = 52.88 ohm , - 2.28 ohm