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.
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