Solving Capacitors Earthed MCQ: V1, V2 Values

[cupid.callin]

Question is in pic ...

Well its a MCQ so options are:

(A) With S1 closed, V1 = 15V and V2 = 20V
(B) With S3 closed, V1 = V2 = 25V
(C) With S1 and S2 closed, V1 = V2 = 0
(D) With S1 and S3 closed, V1 = 30V, V2 = 20V

i know that anything connected to Earth comes to zero potential, but C is not correct answer.

Please help me.

 

[cupid.callin]

some help please?

 

[Phrak]

What you have done so far on this problem?

 

[cupid.callin]

well this is the problem ... i am not understanding where to start

if i close switch S3 will charges flow to each other and neutralize or not?

 

[cupid.callin]

and even i don't know which plate is + and which - ... do i need that?

 

[Phrak]

and even i don't know which plate is + and which - ... do i need that?

That's interesting. I didn't notice that oversight, but it turns out not to matter.

What do you know about current flow and capacitor, and the charge balance on each plate?

 

[cupid.callin]

well i know that in a capacitor current flows via induction, and using Gauss law one can prove that the inner surfaces have equal and opposite charges

 

[Phrak]

OK. That's good. Let's look at a similar and simpler problem. You have one capacitor with a switch on each end and both switches tie to ground. Since both switches go to ground on one side, it's just like they are electrically connected, and we can remove the ground symbols and connect them with a piece of wire.

What happens when only one switch is closed?

 

[cupid.callin]

i would say that its charge will go to the ground ...

 

[tiny-tim]

hi cupid.callin!

(C) With S1 and S2 closed, V1 = V2 = 0
…
i know that anything connected to Earth comes to zero potential, but C is not correct answer.

but with switch S₃ still open, how can the charge on the RHS of C₂ possibly disappear?

 

[Phrak]

The capacitor plates will maintain equal and opposite charge. No charge flows directly from one plate to another across the gap. To get negative charges to leave one plate, an equal and opposite amount of negative charge will have to enter the other plate to maintain neutral charge balance. Each plate requires a current path to do this.

 

[cupid.callin]

i thought that if charge on one capacitor is gone, its potential will be 0

 

[cupid.callin]

The capacitor plates will maintain equal and opposite charge. No charge flows directly from one plate to another across the gap. To get negative charges to leave one plate, an equal and opposite amount of negative charge will have to enter the other plate to maintain neutral charge balance. Each plate requires a current path to do this.

do you want to say that no charge flow will take place because the charges on two plates are attracting each other?

 

[tiny-tim]

i thought that if charge on one capacitor is gone, its potential will be 0

(even if only one plate was charged, there'd still be a potential difference, wouldn't there? but anyway …)

the charge can't get away from the RHS, so if charge is available, it will come to the LHS to balance it out

it's like sticking a metal pole in the ground, then bringing an isolarted charged sphere very close to the pole …

what will happen? ​

 

[cupid.callin]

well the pole will take some charge(or give) to get oppositely charged, in order to be at zero potential

 

[tiny-tim]

yup! and similarly the LHS of C₂, connected to earth, will do exactly the same (or would do, if it didn't already have the correct balancing charge)!

 

[cupid.callin]

so you mean that if i close all the switches ... V1 = 30V and V = 20V

 

[tiny-tim]

so you mean that if i close all the switches ... V1 = 30V and V = 20V

(that isn't one of the MCQ options, but anyway …)

no, because the charge can still move between the RHS of C₁ and the LHS of C₂

 

[cupid.callin]

why? aren't the charges on inner plates in attraction with their outer plates? so they shouldn't move. and we even don't know if inner plates contain opposite or same charge

 

[tiny-tim]

why? aren't the charges on inner plates in attraction with their outer plates?

but the outer charges aren't fixed … they're free to run away to Earth …

if the inner charges want to move, the flighty outer charges aren't going to stop them! …

if you were one of the inner charges, would you want to move?

 

[cupid.callin]

but then what would be the answer?

 

[tiny-tim]

but then what would be the answer?

uhh?

you tell us! ​

 

[cupid.callin]

Hi,

I checked another book and in it the option D:
(D) With [STRIKE]S1 and[/STRIKE] S3 closed, V1 = 30V, V2 = 20V
is given as:
(D) With S3 closed, V1 = 30V, V2 = 20V

and it also says that (D) is correct,
well that makes sense now but if still D was:
(D) With S1 and S3 closed, V1 = 30V, V2 = 20V
it will be still correct, right?

 

[tiny-tim]

Hi,

I checked another book and in it the option D:
(D) With [STRIKE]S1 and[/STRIKE] S3 closed, V1 = 30V, V2 = 20V
is given as:
(D) With S3 closed, V1 = 30V, V2 = 20V

and it also says that (D) is correct,
well that makes sense now but if still D was:
(D) With S1 and S3 closed, V1 = 30V, V2 = 20V
it will be still correct, right?

Yes, if S₃ is closed and S₂ is open, then the charge on the LHS of C₃ can't move, so the charge on the RHS won't move.

Same if S₁ is closed and S₂ is open.

Same if both S₁ and S₃ are closed and S₂ is open.

Are you clear on why now?

 

[cupid.callin]

Yes I'm clear.

Thank you so much for your time!