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NDA 2024
Exam
NDA
Year
2024
Subject
General Ability
Chapter
General Science

NDA 2024 · General Ability · General Science

An infinite combination of resistors, each having resistance R=4 ,...

An infinite combination of resistors, each having resistance R=4ΩR=4 \Omega, is given below. What is the net resistance between the points A and B ? (Each resistance is of equal value, R=4R=4 )

Options

  1. A0Ω0 \Omega
  2. B2+25Ω2+2 \sqrt{5} \Omega
  3. C2+5Ω2+\sqrt{5} \Omega
  4. D∞Ω\infty \Omega

Correct answer

B. 2+25Ω2+2 \sqrt{5} \Omega

Step-by-step solution

Equivalent Resistance, y=R+R∥y⇒y=R+R×yR+y⇒y=R2+Ry+RyR+y⇒Ry+y2=R2+2Ry⇒y2−4y−16=0⇒Req or y=2+25 ohm \begin{array}{r} y=\mathrm{R}+\mathrm{R} \| y \\ \Rightarrow y=\mathrm{R}+\frac{\mathrm{R} \times y}{\mathrm{R}+y} \\ \Rightarrow y=\frac{\mathrm{R}^2+\mathrm{R} y+\mathrm{R} y}{\mathrm{R}+y} \\ \Rightarrow \mathrm{R} y+y^2=\mathrm{R}^2+2 \mathrm{R} y \\ \Rightarrow y^2-4 y-16=0 \\ \Rightarrow \mathrm{R}_{\mathrm{eq}} \text{ or } y=2+2 \sqrt{5} \text{ ohm } \end{array}
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