Question

The Resistance of the series combination of two resistance is S . When they are joined in parallel , the total resistance is P . if S = np, then minimum possible value of n is [AIEEE 2004] ​

Answer 1

Answer:

The minimum possible value of n is 4

Explanation:

Let resistance be R₁ and R₂ and P = R₁R₂ /R₁+ R₂

∴ (R₁ + R₂ ) = n× R₁R₂ /R ₁+ R₂ [∵ S = nP]

Or , (R₁ + R₂ ) ² = n R₁ R₂

=> n = [R₁²+ R₂² + 2R₁ R₂ /R₁ R₂ ]

= [R₁ /R₂ + R₂ /R₁ +2] _____(1)

We know , Arithmetic mean ≥ Geometric mean

R₁ /R₂ + R₂ /R₁ /2 ≥ √R₁/R₂ ×R₂/R₁

=> R₁ /R₂ + R₂ /R₁ ≥ 2

so, from (1) n (minimum value ) = 2+2 = 4 Answer

Answer 2

Answer:

hope it helps u .....................