The effective capacitance between point A and B of the combination of capacitors in an infinite ladder network given below is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2C
For an infinite ladder, removing the first section leaves a ladder that is still infinite and identical to the whole, so the capacitance of the remaining ladder equals the capacitance \( C_{\mathrm{eq}} \) of the whole network.
Replace everything beyond the first section by a single capacitor \( C_{\mathrm{eq}} \), combine it with the capacitors of the first section using the series and parallel rules, and set the result equal to \( C_{\mathrm{eq}} \). This gives an equation in \( C_{\mathrm{eq}} \) alone; for the ladder in the figure its positive solution is
\( \displaystyle C_{\mathrm{eq}} = 2C \)