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capacitors

capacitors

by lokesh sardana -
Number of replies: 2

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Three identical parallel conducting plates A, B and C are placed as shown. Switches S1 and S2 are open, and can connect A and C to earth when closed. +Q charge is given to B. Then which of the following options is/are correct?

(A)   If S1 is closed with S2 open, a charge of amount Q will pass through S1.

(B)   If S2 is closed with S1 open, a charge of amount Q will pass through S2.

(C)   If S1 and S2 are closed together, a charge of amount Q/3 will pass through S1, and a charge of amount 2Q/3 will pass through S2.

(D)   All the above statements are incorrect.       

In reply to lokesh sardana

Re: Capacitors

by Manish Verma -
When S1 is closed with S2 open, the left plate is earthed and the left plate and the middle plate would form a parallel plate capacitor and hence +Q charge from the left plate would go to the earth (-Q charge will stay in the left plate).  This charge will have to pass through S1 as it moves into the earth.

When S2 is closed with S1 open, the discussion is just like the upper one.

When both S1 and S2 are closed we have two parallel plate capacitors connected in parallel holding total charge Q.  Since, capacitance is inversely proportional to distance between the plates and the capacity to store charge is proportional to the capacitance for capacitors in parallel, the right side capacitor can hold double charge in comparison to the left side one. 

The charge in the left capacitor (q) + charge in the right capacitor (2q) = Q
\(\Rightarrow q =\frac{Q}{3}\)

So, q from the left plate goes to the earth and hence passes through S1 and 2q from the right plate goes to the earth and hence passes through S2.
In reply to Manish Verma

Re: Capacitors

by lokesh sardana -
Sir, please explain why 2 plates behave as parallel plates capacitor when one of them is earthed?Is this due to potential difference developed between them or something else.If it is due to potential difference,then isn't there potential diff. between plates B and C?