# When two conductors are connected in series, the total resistance is 5 ohms

When two conductors are connected in series, the total resistance is 5 ohms, and when connected in parallel, 1.2 ohms. What are resistances equal to?

When two conductors are connected in series, the total resistance is calculated by the formula:
Rо = R1 + R2 where Rо is the total resistance, R1, R2 are the resistance of the first and second conductors

According to the condition, with a serial connection, Rо was 5 Ohm:
R1 + R2 = 5 [Ohm]
Let us express the first resistance through the second:
R1 + R2 = 5
R1 = 5 – R2 (1)

When two conductors are connected in parallel, the total resistance is calculated using the formula:
Ro = (R1 * R2) / (R1 + R2)

According to the condition, when connected in parallel, Rо was 1.2 Ohm:
(R1 * R2) / (R1 + R2) = 1.2 (2)
Substitute equation (1) into equation (2)
(R1 * R2) / (R1 + R2) = 1.2
((5 – R2) * R2) / ((5 – R2) + R2) = 1.2
(5 * R2 – R2²) / 5 = 1.2
-R2² + 5 * R2 = 1.2 * 5
-R2² + 5 * R2 = 6
R2² – 5 * R2 + 6 = 0
D = b² − 4ac = 25 – 24 = 1
R2 = (-b ± √D) / (2 * a) = (5 ± 1) / 2
R2 = 3 or R2 = 2

Find R1:
R1 = 5 – R2 = 5 – 3 = 2 [Ohm] (with R2 = 3)
R1 = 5 – R2 = 5 – 2 = 3 [Ohm] (with R2 = 2)

Answer: 2 [Ohm] and 3 [Ohm]

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