What Is the Voltage Across Each Capacitor After Reconfiguration?

[Skirmisher]

Homework Statement

Two capacitors, 6uF and 14uF, ae conncted in series across an 18 V battery. They are carefully disconnected so that they are not discharged and they are then reconnected to each other, with postive plate to positive plate and negative plate to negative plate.

Find the resulting potential difference across each capacitor after they are connected. Answer in units of V.

Homework Equations

C=Q*V

For Plates in series:
Q1 = Q2 = Q
V1+V2=V(total)

The Attempt at a Solution

The part that confuses me is when it say that they reconnect the plates "positive plate to positive plate and negative plate to negative plate." I thought maybe it was recongifuring them into a parallel series which would mean the voltage was 18 V or 9 V if the battery was taken out of the loop but since both those answers are incorrect that doesn't seem to be the case.

 

[jbsteele]

So, I'm thinking that it means they are in series and the charge must remain the same. So, Q1 = Q2 = Q and V1+V2=V(total). If this is the case then:C1 = 6uFC2 = 14uFV1 + V2 = 18VQ1 = Q2 = QC1*V1 = C2*V26uF*V1 = 14uF*V2V1 = 2.3 V and V2 = 15.7 V

 

[baba89]

I would approach this problem by first analyzing the initial setup and the reconfiguration. In the initial setup, the two capacitors are connected in series, meaning that they share the same amount of charge and the total voltage is divided between them. This can be represented by the equation V(total) = V1 + V2.

When the capacitors are reconfigured, they are connected with positive plates to positive plates and negative plates to negative plates. This essentially creates a parallel connection, where the voltage across each capacitor is equal and the total charge is divided between them. This can be represented by the equation Q(total) = Q1 + Q2.

Using the equation C = Q*V, we can rearrange it to V = Q/C. Since the total charge is divided between the two capacitors, we can substitute Q(total) = Q1 + Q2 into the equation and get V(total) = (Q1 + Q2)/(C1 + C2).

Substituting the given values for C1, C2, and V(total) = 18 V, we can solve for Q1 and Q2. Then, using the equation V1 = Q1/C1 and V2 = Q2/C2, we can calculate the resulting potential difference across each capacitor after they are connected.

In summary, the resulting potential difference across each capacitor after they are connected will be determined by the total charge and the capacitance of each capacitor in the reconfigured parallel connection.