Question

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.

(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.

Answer 1

Correct Answer is: (a, b, & c)

When either A or C is earthed (but not both together), a parallel-plate capacitor is formed with B, with +Q charges on the inner surfaces. [The other plate, which is not earthed, plays no role]. Hence charge of amount +Q flows to the earth.

When both are earthed together, A and C effectively become connected. The plates now form two capacitors in parallel, with capacitances in the ratio 1 : 2, and hence share charge Q in the same ratio.