Q.

Five plates are arranged as shown in the figure and connected across a battery of emf V. The separation between each plate is d and surface area of each plate is A.
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a

Equivalent capacity between P and Q is ε0A5d

b

Equivalent capacity between P and Q is 3ε0A5d

c

Charge on plate 1 is  ε0AV5d

d

Charge on plate 3 is 3ε0AV5d

answer is B, C, D.

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Detailed Solution

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C=0d 1Ceq=1C+23C=53C    Option (B) is correct. Option (A) is wrong.
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Total charge, Q=CeqPQV=3Aε0V5d
In parallel combination, charge is proportional to capacitance.
Charge on plate 1, C/23C/2×Q=Q3=133Aε0V5d=Aε0V5d   

Option (C) is correct.
Charge on plate 3 in lower branch =Aε0V5d
Charge on plate 3 in upper branch =QAε0V5d=2Aε0V5d
Total charge on plate 3 =Q=3Aε0V5d  Option (D) is correct.
 

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