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when two resistors are connected in sereies are connected in series, their effective resistance is 80 Ohm. When they are connected in parallel, their effective resistance is 20 Ohm. What are the values of the two resistances? |
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Answer» and R2 be the two resistances. When they are in PARALLEL, resultant RESISTANCE Rp is given by1/Rp = 1/R1 + 1/R2Rp = R1R2/(R1 + R2)2 = R1R2/(R1 + R2)2(R1 + R2) = R1R2When they are in series effective resistance Rs = R1 + R29 = R1 + R2 ⇒ R2 = 9 - R12 x 9 = R1 R2 = R1 (9 - R1) = 9R1 - R12.18 = 9R1 - R12.R12 - 9R1 + 18 = 0Solve this quadratic equation. You will get R1 = (9 ± √(81 - 4 x 1 x 18))/2 = (9 ± √9)/2 = (9 ± 3)/2R1 = 3 ohm or 6 ohmIf R1 = 3 ohm, R2 = 6 ohm and vice versa. |
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