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CUET · MATHS · PYQ PAPER 2023

The combined resistance \(R\) of two resistors \(R_1\) and \(R_2\left(R_1, R_2>0\right)\) is given by\(\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}\) if \(R_1+R_2=C\) (a constant). The maximum resistance \(R\) is obtained when

  1. A \(R_1=R_2\)
  2. B \(R_1=2 R_2\)
  3. C \(2 R_1=R_2\)
  4. D \(R_1=3 R_2\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(R_1=R_2\)

Step-by-step Solution

Detailed explanation

\(R = \frac{R_1 R_2}{R_1 + R_2}\) \(R = \frac{R_1 R_2}{C}\) \(R = \frac{R_1 (C - R_1)}{C} = R_1 - \frac{R_1^2}{C}\) \(\frac{dR}{dR_1} = 1 - \frac{2R_1}{C}\) \(\frac{dR}{dR_1} = 0 \implies 1 = \frac{2R_1}{C} \implies C = 2R_1\) \(R_1 + R_2 = 2R_1 \implies R_1 = R_2\)
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