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when two resistors of resistance R1 and R2 are connected in parallel the net resistance is 3 ohm when connected in series its value is 60 ohm calculate the value of R1 and R2 |
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Answer» Answer: R₁ and R₂ are 57 Ω or 3 Ω and 3 Ω or 57 Ω respectively. Explanation: There are two resistors, R₁ and R₂. They are connected parallel which MEANS equivalent RESISTANCE will be Rₚ which is EQUAL to 3 Ω. When they are connected in series then equivalent resistance Rₛ is equal to 60 Ω.
→ 1/3 = (R₁ + R₂)/R₁R₂ → 1/3 = 60/R₁R₂ → R₁R₂ = 180 → R₂ = 180/R₁ → 60 = R₁ + 180/R₁ → 60 = (R₁² + 180)/R₁ → R₁² - 60R₁ + 180 = 0 → D = b² - 4ac → D = 3600 - 720 → D = 2880 → R₁ = (60 ± √2880)/2 → R₁ = (60 ± 54)/2 → R₁ = 57 Ω or 3 Ω→ R₂ = 60 - 57 → R₂ = 3 Ω or 57 Ω |
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