The equivalent resistance of two resistors connected in series is 6 Ω

The Equivalent Resistance Of Two Resistors Connected In Series Is Physics QuestionThe Equivalent Resistance Of Two Resistors Connected In Series Is Physics Question

The equivalent resistance of two resistors connected in series is 6 Ω and their parallel equivalent resistance is 4/3Ω. What are the values of resistances?

Options

(a) 4Ω,6Ω
(b) 8Ω,1Ω
(c) 4Ω,2Ω
(d) 6Ω,2Ω

Correct Answer:

4Ω,2Ω

Explanation:

Let the values of resistance be R₁ and R₂, respectively.
When R₁ and R₂ resistance are series, then
R₁ + R₂ = 6 (according to question) ——(i)
When R₁ and R₂ resistance are parallel, then
R₁R₂ / R₁+R₂ = 4 / 3 ——(ii)
From the equation (i), we get
R₁R₂ / 6 = 4 / 3 ⇒ R₁R₂ = 4 × 3 ⇒ R₁R₂ = 8 —–(iii)
We know that,
R₁ – R₂ = √[(R₁ + R₂)² – 4R₁R₂] = √[36 – 4 × 8] = √4 = 2
From equation (i) and (iv), we get
R₁ = 4 Ω, R₂ = 2 Ω

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