assume that, for the two resistors in series, the second has a resistance that i

Question

assume that, for the two resistors in series, the second has a resistance that is three times the resistance of the first one in the series. The single resistor has a resistance that is 6 ohms more than the resistance of the first resistor in series, and the total resistance of the circuit is 4 ohms. Write an equation to model this situation, and solve this equation.

Explanation / Answer

let R1 an R2 are in series R2 = 3R1 given R3 is in parallel the series combination R3 = R1 + 6 given Rnet = R3(R1+R2)/(R1+R2+R3) = (R1+6)(4R1)/(5R1+6) = 4 =>4R1^2 + 4R1 -24 = 0 ?R1 = -2.4365 and 1.4365 but R1 cant be negative ?R1 = 1.4365 ohms R2 = 3*1.4365 = 4.3095 ohms R3 = 1.4365 + 6 = 7.4365 ohms

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