50 capacitors each of capacitance 'C' are connected as shown in figure. Calculate the equivalent capacitance between the point 'A' and 'B'.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{50}{49}C \)
The capacitors \( C_1 \) to \( C_{49} \) are joined one after the other round the ring, so they are in series between A and B. The remaining capacitor \( C_{50} \) is connected directly between A and B, so it is in parallel with that chain.
Chain of 49 capacitors in series
\( \displaystyle \frac{1}{C_s} = \underbrace{\frac{1}{C} + \frac{1}{C} + \cdots + \frac{1}{C}}_{49\text{ terms}} = \frac{49}{C} \Rightarrow C_s = \frac{C}{49} \)
In parallel with \( C_{50} \)
\( \displaystyle C_{\mathrm{eq}} = C + \frac{C}{49} = \frac{50}{49}C \)