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Capacitance of Parallel Plate Capacitor

Question

Five identical plates are connected across a battery as shown. If the charge on plate 1 be +q, then the charges on the plates 2, 3, 4 and 5 are:

$- q, + q, - q, + q$
$- 2 q, + 2 q, - 2 q, + q$
$- q, + 2 q, - 2 q, + q$
$n o n e o f t h e a b o v e$

A

- q, + q, - q, + q

B

- 2 q, + 2 q, - 2 q, + q

C

- q, + 2 q, - 2 q, + q

D

n o n e o f t h e a b o v e

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Solution

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As the plate 2 is common plate for two capacitors and connected to the negative terminal of battery so its charge should be $- (q + q) = - 2 q$ .
Similarly plate 3 is also common plate between two capacitors and connected to the positive terminal of battery so its charge should be $+ (q + q) = + 2 q$ .
Similarly for plate 4, charge on it $= - (q + q) = - 2 q$
Plate 5 is not common plate between two capacitors and connected to positive end of battery. Thus its charge $= + q$

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