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Q.

Five identical capacitor plates, each of area A, are arranged such that the adjacent plates are at a distance d apart. The plates are connected to a source of emf V as shown in figure. Match the following.

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 Column I Column I
i)Charge on plate 1p)2ε0AV/d
ii)Charge on plate 4q)+ε0AV/d
iii)Potential difference between plates 2 and 3r)Zero
iv)Potential difference  between plates 1 and 5s)V

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a

i-p, ii-r, iii-q, iv-s

b

i-q, ii-p, iii-s, iv-r

c

i-q, ii-q, iii-r, iv-s

d

i-p, ii-q, iii-r, iv-s

answer is D.

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Detailed Solution

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These five plates constitute four identical capacitors in parallel, each of capacity ε0A/d. Now, as plate 1 is connected to the positive terminal of the battery and is a part of one capacitor only, so charge on it is q1=+(ε0AVd)

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So, i-b.
However, plate 4 is connected to the negative terminal of the battery and is common to the two identical capacitors in parallel. So,  q4=(2ε0AVd)
Hence, ii-a.
From the circuit, it is obvious that between the plates 2 and 3, the battery is connected, so the potential difference will be V. Plates 1 and 5 get connected through connecting wire, so the potential difference between I and 5 is zero.    

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