Six identical capacitors, each of capacitance C, are connected as follows: two of them in parallel are joined in series with a third one, and two such groups of three capacitors are connected in parallel between the points A and B. The equivalent capacitance between A and B is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4C/3
Capacitors in parallel have the same potential difference and their charges add, so their capacitances add. Capacitors in series carry the same charge and their potential differences add, so the reciprocals of their capacitances add.
The two capacitors in parallel in each group give:
\( \begin{aligned} C_{\mathrm{p}} &= C+C \\ &= 2C \end{aligned} \)
This \( 2C \) is in series with the third capacitor \( C \):
\( \begin{aligned} \frac{1}{C_{\mathrm{g}}} &= \frac{1}{2C}+\frac{1}{C} \\ &= \frac{3}{2C} \end{aligned} \)
\( \displaystyle C_{\mathrm{g}}=\frac{2C}{3} \)
The two identical groups are in parallel between A and B:
\( \begin{aligned} C_{AB} &= \frac{2C}{3}+\frac{2C}{3} \\ &= \frac{4C}{3} \end{aligned} \)