How Does Reconnecting Charged Capacitors Affect Their Charge Distribution?

[minimario]

Homework Statement

Capacitors $C_1 = 4 \mu F$ and $C_2 = 2 \mu F$ are charged as a series combination across a $100V$ battery. The two capacitors are disconnected from the battery and from each other. They are then connected positive plate to positive plate and negative plate to negative plate. Calculate the resulting charge on each capacitor.

Homework Equations

$C = \frac{Q}{V}$
Parallel: Same Voltage
Series: Same Charge

The Attempt at a Solution

Is this correct:

Since the two capacitors are connected in series, their resulting capacitance is $\frac{4}{3} \mu F$, so the charge on each capacitor is $133.33 \mu C$; therefore, when they are connected pos. to pos. and neg. to neg., both charges will be $133.33 \mu C$.

 

[gneill]

Since the two capacitors are connected in series, their resulting capacitance is $\frac{4}{3} \mu F$, so the charge on each capacitor is $133.33 \mu C$; therefore, when they are connected pos. to pos. and neg. to neg., both charges will be $133.33 \mu C$.

The capacitors are of different size so with the same initial charge they will have different voltages. When they are then connected in parallel as described, the voltage difference must be reconciled by charges moving to eliminate the potential differences. But total charge must be conserved...

 

[minimario]

How do you know they are "connected in parallel as described": I thought it's series?

 

[gneill]

How do you know they are "connected in parallel as described": I thought it's series?

The problem statement says: "They are then connected positive plate to positive plate and negative plate to negative plate."

 

[minimario]

How do you know that is parallel?

 

[gneill]

How do you know that is parallel?

Technically you can interpret the result as either series or parallel connection since it satisfies both definitions. But in this case it's convenient to look at the connection as being parallel so that you can take advantage of the fact that parallel components share the same potential difference.

 

[minimario]

No, you cannot look at the connection as being series, because the charge is not the same...

 

[ehild]

No, you cannot look at the connection as being series, because the charge is not the same...

In case of series capacitors, the charges on the connected plates are of equal magnitude, but of opposite sign so the net charge of the connected plates is zero. In this case, they are of the same sign, .

 

[SammyS]

How do you know they are "connected in parallel as described": I thought it's series?

The problem statement says: "They are then connected positive plate to positive plate and negative plate to negative plate."

How do you know that is parallel?

Technically you can interpret the result as either series or parallel connection since it satisfies both definitions. But in this case it's convenient to look at the connection as being parallel so that you can take advantage of the fact that parallel components share the same potential difference.

No, you cannot look at the connection as being series, because the charge is not the same...

The above exchange strikes me as being rather odd.

 

[gneill]

No, you cannot look at the connection as being series, because the charge is not the same...

Series vs parallel is a matter of physical connection topology. How charge distribution behaves when the pair is connected to an external source is another matter (related, but not defining).