The resistance of the series combination of two resistances is S . When they are joined in parallel, the total resistance is P . If S = nP , then the - Physics MCQ AIEEE 2004 2026 | ExamTest.live

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The resistance of the series combination of two resistances is S . When they are joined in parallel, the total resistance is P . If S = n P, then the minimum possible value of n is:

Solution & Step-by-step Explanation

Let the two resistances be R_{1} and R_{2} . S = R_{1} + R_{2} P = \frac{R _{1} R _{2}}{R _{1} + R _{2}} Given S = n P ⟹ R_{1} + R_{2} = n \frac{R _{1} R _{2}}{R _{1} + R _{2}} ⟹ (R_{1} + R_{2})^{2} = n R_{1} R_{2} . n = \frac{R _{1}^{2} + R _{2}^{2} + 2 R _{1} R _{2}}{R _{1} R _{2}} = \frac{R _{1}}{R _{2}} + \frac{R _{2}}{R _{1}} + 2 Using AM-GM inequality, x + 1/ x \geq 2 .So, n_{min} = 2 + 2 = 4 . This occurs when R_{1} = R_{2} .

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The resistance of the series combination of two resistances is S . When they are joined in parallel, the total resistance is P . If S = n P, then the minimum possible value of n is:

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