A resistance r1=12ohms is connected in series with another resistance r2= 8 ohms. What resistance r3 must be connected in parallel with the combination of r1 and r2 so that the equivalent resistance is equal to the resistance r1?

Answer 1

r1 = [(r1 + r2) * r3] / (r1 + r2 + r3)

plug in values and solve for r3

Answer 2

Given:
R1 = 12 ohms.
R2 = 8 ohms.

R1 + R2 = 12 + 8 = 20 ohms.
(R3*20)/(R3+20) = R1.
(R3*20)/(R3+20) = 12.
20R3 = 12R3 + 240,
R3 = ?