Four identical thin, square metal sheets, S1, S2, S3 and S4, each of side a are kept parallel to each other with equal distance d ( a) between them, as shown in the figure. Let C0= 0 a2/d, where 0 is the permittivity of free space. [figure] Match the quantities mentioned in List-I with their values in List-II and choose the correct option.
- P → 3; Q → 2; R → 4; S → 5
- P → 2; Q → 3; R → 2; S → 1
- P → 3; Q → 2; R → 4; S → 1
- P → 3; Q → 2; R → 2; S → 5
Answer
(3) P → 3; Q → 2; R → 4; S → 1
Solution
Adjacent sheets form three capacitors, each C0: C12, C23, C34.
(P) S1–S4, S2,S3 floating: three in series ⇒ C03 → 3.
(Q) S2 shorted to S3: C23 shorted out; C12 and C34 in series ⇒ C02 → 2.
(R) Nodes S1, X=\S2,S4\, S3: C12 between S1 and X; C23 and C34 both between X and S3 (parallel, 2C0). Series: C0 2C03C0= 2C03 → 4.
(S) Nodes A=\S1,S3\, B=\S2,S4\: all three capacitors lie between A and B ⇒ parallel, 3C0 → 1.
Answer: (C)