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Question 27

The equivalent capacitance between points $$A$$ and $$B$$ in below shown figure will be ______ $$\mu$$F.


Correct Answer: 6

$$\text{The first, second, and third capacitors are connected in parallel between terminal } A \text{ and node } P.$$

$$\text{The fourth and fifth capacitors are connected across the same node } P $$ on both sides, which short-circuits them

$$\text{The sixth capacitor is connected in series between node } P \text{ and terminal } B.$$

Parallel combination of the first 3 active capacitors: $$C_p = 8 + 8 + 8 = 24\ \mu\text{F}$$

Equivalent capacitance of the entire network with the final $$8\ \mu\text{F}$$ capacitor in series:

$$C_{AB} = \frac{C_p \times 8}{C_p + 8} = \frac{24 \times 8}{24 + 8} = \frac{24 \times 8}{32} = 6\ \mu\text{F}$$

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