Four capacitors are connected in a circuit as shown in the figure. The equivalent capacitance between P and Q will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 5\,\mu\mathrm{F} \)
Capacitors in parallel add directly; capacitors in series combine by reciprocals. Readings from the figure: in the upper path two \( 2\,\mu\mathrm{F} \) capacitors are in parallel, and this pair is in series with \( 12\,\mu\mathrm{F} \); the lower path is a single \( 2\,\mu\mathrm{F} \) capacitor, in parallel with the whole upper path.
\( \displaystyle C_1 = 2 + 2 = 4\,\mu\mathrm{F} \)
\( \displaystyle C_{\text{upper}} = \frac{C_1 \times 12}{C_1 + 12} = \frac{4 \times 12}{4 + 12} = \frac{48}{16} = 3\,\mu\mathrm{F} \)
\( \displaystyle C_{PQ} = C_{\text{upper}} + 2 = 3 + 2 = 5\,\mu\mathrm{F} \)