Question

when two resistors are connected in series their effective resistance is 80ohm when they are connected in parallel their effective resistance is 20ohm. what are the values of the two resistance?

Answer 1

Answer

When connected in series 
R₁ + R₂ = 80 Ω ………[1]

When connected in parellel
R₁R₂ / (R₁ + R₂) = 20 Ω ………[2]

Equation [2] can also be written as
R₁R₂ / 80 = 20 ………[∵ From (1)]
R₁R₂ = 1600 
R₁ = 1600 / R₂ 

Substitute this value in equation [1]
(1600 / R₂) + R₂ = 80
R₂² - 80R₂ + 1600 = 0

Solve above polynomial equation
We will get R₂ = 40 Ω
If R₂ is 40 Ω then from equation [1] R₁ is also 40 Ω

Therefore,
Values of two resistance is 40 Ω

Answer 2

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Here's your Answer....

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When connected in series
R₁ + R₂ = 80 Ω ………[1]

When connected in parellel
R₁R₂ / (R₁ + R₂) = 20 Ω ………[2]

Equation [2] can also be written as
R₁R₂ / 80 = 20 ………[∵ From (1)]
R₁R₂ = 1600
R₁ = 1600 / R₂

Substitute this value in equation [1]
(1600 / R₂) + R₂ = 80
R₂² - 80R₂ + 1600 = 0

Solve above polynomial equation
We will get R₂ = 40 Ω
If R₂ is 40 Ω then from equation [1] R₁ is also 40 Ω

Therefore,
Values of two resistance is 40 Ω.
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