Which Statements Are True for Capacitors in Earthed Circuits?

[Tanishq Nandan]

Homework Statement

For the curcuit shown in figure,which of the following statement is true?
A)with S1 closed, V1=15V, 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

Homework Equations

▪Q=CV,
where Q and V are the charge and potential of a capacitor,C it's capacitance
▪Earthing a circuit means that potential at that point is zero.

The Attempt at a Solution

I know how to do this kind of sums,writing potential 0 on one side,assuming V on the other side,assuming charges on the capacitor,using Q=CV..
BUT
how do I find the polarity of the capacitors??
V1=30 could mean either the left or right plate is the negative one,I thought that if it isn't given in the question,maybe it won't matter,but it does (according to me,at least)
Help appreciated..

 

[Hesch]

The capacitors are coupled in series. All the switches must be closed before the charges can get away ( rearrange ).

None of the suggestions have all switches closed, so D) is correct because the voltages V1, V2 are unchanged ( no change in the location of the charges ).

Don't bother about the polarities.

 

[cnh1995]

To change the voltages, a current should flow through the capacitors. Is that possible in any of the options?

 

[Tanishq Nandan]

Umm..won't closing either S1 or S2 cause some charge from the corresponding plate to flow into the Earth or from the Earth to the plates?

Or closing only S3?won't that cause any current (movement of charges)??

 

[cnh1995]

Umm..won't closing either S1 or S2 cause some charge from the corresponding plate to flow into the Earth or fromt he Earth to the plates?

No.
And unless it is specifically mentioned in the problem, the symbol does not actually represent 'earth'. It represents 'ground', which is a common reference node (0V point) in electrical circuits.

 

[Tanishq Nandan]

Ooo,k,thanks.

 

[Hesch]

If you have to change the voltages across a capacitor, you must have current flowing through this capacitor.

If just one switch is open, no current can pass through the serial connection.

Remember Kirchhoffs current law ( KCL ).

 

[scottdave]

The side which is connected to "ground" will be at 0 Volts, but that doesn't mean the other side of the cap will be zero.
If 2 capacitors are connected together in series (either through the switch S3, or through S1,S2 and the Earth/ground) then the charges will equalize so that each cap has the same amount of charge. You can figure the amount of charge before, on each. Then split that charge evenly between them, to see what the new voltages are.

You are correct, that they should have put some polarity on those voltages. You need to assume one, and see how that figures out. I have an idea of which answer is correct, though.

 

[Tanishq Nandan]

The side which is connected to "ground" will be at 0 Volts, but that doesn't mean the other side of the cap will be zero.
If 2 capacitors are connected together in series (either through the switch S3, or through S1,S2 and the Earth/ground) then the charges will equalize so that each cap has the same amount of charge. You can figure the amount of charge before, on each. Then split that charge evenly between them, to see what the new voltages are.

You are correct, that they should have put some polarity on those voltages. You need to assume one, and see how that figures out. I have an idea of which answer is correct, though.

That is the kind of approach I usually have towards these problems (quantitative),but Hesch and cnf1995 pointed out something so that it doesn't even require a pen to get the answer :)

 

[scottdave]

If you have to change the voltages across a capacitor, you must have current flowing through this capacitor.

If just one switch is open, no current can pass through the serial connection.

Remember Kirchhoffs current law ( KCL ).

Kirchhoff's Current Law states that sum of currents entering a node, must equal the currents exiting the node.

I propose a different scenario: say one capacitor is charged and the other has no charge. If there are a bunch of excess electrons on one plate of a capacitor, and you close a switch, which allows a path to the uncharged cap, will electrons flow away from the excess charge. This is basic electrostatics. Electrons repel each other and if there is an easy path for them to get away, then they will.

As for this case, I can figure the amount of charge on each cap, without a pencil, and figure what will happen.

 

[Tanishq Nandan]

But both the capacitors have a charge of 60 microcoulombs..

 

[scottdave]

But both the capacitors have a charge of 60 microcoulombs..

Yes, since the charge is the same, the electrons are in equilibrium, so they will have stay where they are with the switches open or closed.