RRC Circuit - Capacitor Charge?

[bchubz]

Homework Statement

http://www.webassign.net/hrw/hrw7_27-76.gif
The circuit in the figure shows a capacitor, two ideal batteries, two resistors, and a switch S. Initially S has been open for a long time. If it is then closed for a long time, what is the charge (in Coulombs) on the capacitor? Assume that the batteries have emfs of ε1 = 1.50 V and ε2 = 8.10 V and that C = 7.00 μF, R1 = 0.18 Ω, R2 = 0.44 Ω.

Homework Equations

Kirchoff's voltage laws

The Attempt at a Solution

I tried C*(V1+V2) = Q. This isn't correct, and not exactly sure where to go next.

 

[berkeman]

Homework Statement

http://www.webassign.net/hrw/hrw7_27-76.gif
The circuit in the figure shows a capacitor, two ideal batteries, two resistors, and a switch S. Initially S has been open for a long time. If it is then closed for a long time, what is the charge (in Coulombs) on the capacitor? Assume that the batteries have emfs of ε1 = 1.50 V and ε2 = 8.10 V and that C = 7.00 μF, R1 = 0.18 Ω, R2 = 0.44 Ω.

Homework Equations

Kirchoff's voltage laws

The Attempt at a Solution

I tried C*(V1+V2) = Q. This isn't correct, and not exactly sure where to go next.

Because the two battery voltages are unequal, there will be a steady-state current in the long term. After stabilization, there will be no current through the cap, and a constant voltage across the cap. You can find that voltage by writing a loop equation around the outer loop to find the loop current, and then calculate what the voltages are at points going around the loop.

 

[bchubz]

Great thanks! I just needed a little nudge.