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Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Current in Conductors

Consider an infinite ladder constructed using 1 and 2 resistors, as shown in the figure. Determine the effective resistance between points A and B .

Options

  1. A3
  2. B2
  3. C1
  4. D2.5

Correct answer

B. 2

Step-by-step solution

Let the effective resistance of the infinite ladder between points A and B be R . Since the ladder is infinite, removing the first repeating unit (one 1 resistor in series and one 2 resistor in parallel) leaves an identical infinite ladder across the next nodes. Therefore, the resistance of the remaining infinite ladder is also R . The equivalent circuit can be simplified to a 1 resistor in series with the parallel combination of a 2 resistor and R . The equation for the equivalent resistance is: R = 1 + 2R 2 + R S

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