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A circuit is connected as shown in the figure with the switch S open. When the switch is closed the total amount of charge that flows from $Y$ to $X$ is?

(A) $0$

(B) 54$\mu$C

(C) 27 $\mu$C

(D) 81 $\mu$C

My attempt:

1) Figure out initial charges on both capacitors. (18 $\mu$C on both)
2) Figure out final charges on both capacitors. (9 and 36 $\mu$C on left & right capacitors respectively)

My problem:

How does the charge move around? What directions do they take?

Attempt at this problem:

When a capacitor is charged, conventional current flows into the positive terminal of the capacitor, and when the capacitor is discharged, current flows out of the positive terminal.

So, if positive charge enters the positive terminal, charges the capacitor, then exit of positive charge from negative terminal should charge the capacitor as well? Then, if positive charge exits from positive terminal, discharging the capacitor, then entrance of positive charge from negative terminal should discharge the capacitor?

If I utilize this logic here, +9$\mu$C (micro-coloumbs) flows from $Y$ to $X$ to the left capacitor (9$\mu$C is lost by this capacitor). Then if +18$\mu$C flows from $Y$ to $X$ to the right capacitor, the charge on it goes to 36$\mu$C (final) from the 18$\mu$C (initial).

Hence total charge flown from $Y \rightarrow X$ is $9 + 18 = 27\mu$C (which is the correct answer to this question).

Is this logic correct? If not, is this an OK analogy to the correct idea?

Questions taken from: JEE(A) 2007 (Part - 1)

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  • $\begingroup$ Yes you can use this analogy. For Jee adv purpose another way of solving this problem is considering second plate of capacitor A and first plate of capacitor B as an isolated system(meaning there is no direct source of charge like a battery to these plates) , for isolated system of plates we can use conservation of charge. Initial charge on system is 0 and final is 36-9=27 .Hence charge flown from Y to X is 27. $\endgroup$ – Vaishakh Sreekanth Menon Mar 19 at 14:15
  • $\begingroup$ Sounds interesting Vaishakh; but could you explain further on what you said? How were you able to consider the 2 plates as an isolated system? I understood everything else other than the assumption itself. $\endgroup$ – McSuperbX1 Mar 20 at 11:49

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