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

  1. A. 0 \Omega
  2. B. 2+2\sqrt{5} \Omega
  3. C. 2+\sqrt{5} \Omega
  4. D. 8 \Omega

Correct Answer: B. 2+2\sqrt{5} \Omega

Explanation

For an infinite ladder, the equivalent resistance R_{eq} satisfies R_{eq} = R + \frac{R \cdot R_{eq}}{R + R_{eq}}. Solving this quadratic equation yields R_{eq} = \frac{R(1+\sqrt{5})}{2}. Substituting R=4 \Omega gives 2+2\sqrt{5} \Omega.

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