I am given two circuits, each with two capacitors and a switch. Capacitor 1 is initially charged. I am asked to find the final charge in each capacitor after the system reaches equilibrium.
In P1 I set the final voltage of each capacitor equal to each other and I get
Q1/C1 = Q2/C2 Q1 + Q2 = Q0
subsituting Q2 = Q0  Q1 and solving, i get
Q1 = (2/5)*Q0 and Q2 = (3/5)*Q0
But when the resistor is included, I cannot figure out what will happen. There are two things that do not add up to me:
The voltage between the terminals of both capacitors will be equal again
The total charge Q0 will be the same.
The potential energy of the system will be lower than it was at t=0 due to the resistor dissipating some of the energy.
It seems like I should use the same method as p1 and set the voltages equal to each other, but I know that in part p1 the potential energy is conserved but in p2 some energy is dissipated.
In P1 I set the final voltage of each capacitor equal to each other and I get
Q1/C1 = Q2/C2 Q1 + Q2 = Q0
subsituting Q2 = Q0  Q1 and solving, i get
Q1 = (2/5)*Q0 and Q2 = (3/5)*Q0
But when the resistor is included, I cannot figure out what will happen. There are two things that do not add up to me:
The voltage between the terminals of both capacitors will be equal again
The total charge Q0 will be the same.
The potential energy of the system will be lower than it was at t=0 due to the resistor dissipating some of the energy.
It seems like I should use the same method as p1 and set the voltages equal to each other, but I know that in part p1 the potential energy is conserved but in p2 some energy is dissipated.
Attachments

32.6 KB Views: 89