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Q.

For the given circuit shown in figure, which of the following statements is/are correct.

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a

The equivalent capacitance between point 1 and 3 is 15C14

b

The equivalent capacitance between points 3 and 5 is 14C15

c

The equivalent capacitance between points 1 and 2 is  15C11

d

The equivalent capacitance between point 3 and 6 is 5C3

answer is A, B, C.

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Detailed Solution

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Answer: Options (a), (b) and (c) are correct

All capacitors have value C. Below are the equivalent capacitances:

(a) Between points 1 and 2:

Equivalent capacitance = 15/11 · C. (Correct) — found by applying 1 V between 2 and 1 and calculating total charge.

(b) Between points 3 and 6:

Equivalent capacitance = 5/3 · C. (Correct) — put 1 V between 3 and 6 and evaluate charges on the network.

(c) Between points 1 and 3:

Equivalent capacitance = 15/14 · C. (Correct) — result from the same node-voltage method or careful reduction.

(d) Between points 3 and 5:

Option (d) claims 14/15 · C, which is incorrect. The actual value (by calculation) is 15/14 · C.

A reliable way is to apply 1 V across the chosen terminals, solve node-voltage relations to find charges on capacitors and sum the total charge Q. Then Ceq=Q (since V=1). This avoids mistakes in series/parallel reductions for symmetric networks.

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