The equivalent capacitance of an infinite ladder network of capacitors, where each repeating section consists of a series capacitor and a shunt parallel capacitor , is:

Answer and explanation

Correct answer: B.

**Answer: .
  1. Step 1: Since the ladder is infinite, removing the first repeating section leaves the remainder with identical equivalent capacitance .
  2. Step 2: The first section consists of series capacitor followed by the parallel combination of and across the output terminals.
  3. Step 3: The equivalent capacitance satisfies: $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2 + C_{eq}} \implies C_{eq} = \frac{C_1(C_2 + C_{eq})}{C_1 + C_2 + C_{eq}}.
  4. Step 4: Substitute and : $C_{eq} = \frac{1(2 + C_{eq})}{1 + 2 + C_{eq}} = \frac{2 + C_{eq}}{3 + C_{eq}}.
  5. Step 5: Multiply out: .
Why not the others: is the shunt capacitance value; is obtained from an incorrect quadratic formulation; divides by 2.

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