QQuestion
When two conductors are connected in series, the equivalent resistance is 25 Ω, and when connected in parallel, the equivalent resistance is 6 Ω. Determine the resistance of each conductor.
✓Answer
Let the resistances be R₁ and R₂.
For series combination:
R₁ + R₂ = 25 Ω …(1)
For parallel combination: 6 = \frac{\text{R₁R₂}}{\text{R₁}+\text{R₂}}
Using (1),
6 = \frac{\text{R₁R₂}}{25}
Therefore,
R₁R₂ = 150 …(2)
From (1), R₂ = 25 − R₁
Putting in (2), R₁(25 − R₁) = 150
25R₁ − R₁² = 150
⇒ R₁² − 25R₁ + 150 = 0
⇒ R₁² − 15R₁ − 10R₁ + 150 = 0
⇒ R₁(R₁ − 15) − 10(R₁ − 15) = 0
⇒ (R₁ − 15)(R₁ − 10) = 0
⇒ R₁ = 15 Ω or 10 Ω
Therefore, R₁ = 10 Ω, R₂ = 15 Ω
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