The effective capacitance between points X and Y in the following network is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (4 ÷ 3) C
Capacitors joined between the same two points are in parallel and their capacitances add; capacitors in series combine as \( C_1C_2/(C_1 + C_2) \) for a pair. Reduce the network group by group.
Upper branch: the top-left capacitor and the one just below it are connected between the same two points, so together they give 2C. This 2C is in series with the top-right capacitor.
\( \displaystyle C_{\mathrm{upper}} = \frac{2C \times C}{2C + C} = \frac{2C}{3} \)
Lower branch: the two capacitors on the right are in parallel, giving 2C, and this is in series with the bottom-left capacitor.
\( \displaystyle C_{\mathrm{lower}} = \frac{C \times 2C}{C + 2C} = \frac{2C}{3} \)
Both branches connect X to Y, so they are in parallel.
\( \displaystyle C_{\mathrm{XY}} = \frac{2C}{3} + \frac{2C}{3} = \frac{4C}{3} \)