# Final electric potential difference in a circuit with two capacitors

Gold Member
Homework Statement:
FIGURE ATTACHED BELOW
##C_{1}=2.00\mu F, q_{1}=6.00\mu C, C_{2}=8.00\mu F, q_{2}=12.0\mu C##
The circuit gets closed and charge flows until the two capacitors have the same electric potential difference ##V_{F}## across its terminals.
-calculate ##V_{F}##.
Relevant Equations:
##q=CV##

So, each capacitor must have a different potential difference, given by its capacity and charge... this would cause charge and current accordingly to flow in the circuit.
But how do I determine the final potential difference, which would of course be the same for both of them? I have tried writing down something, which I've found out to be unuseful to solve this problem.

gneill
Mentor
The capacitors start out with different potentials across them. What are they?

If some amount of charge, say ##\Delta q## moves from the higher potential capacitor to the lower potential one, what expressions can you write for those new potentials?

Gold Member
The capacitors start out with different potentials across them. What are they?

If some amount of charge, say ##\Delta q## moves from the higher potential capacitor to the lower potential one, what expressions can you write for those new potentials?
Ok, so, since ##V_{1}>V_{2}##, I'll have a ##\Delta q## transferring from 1 to 2, so the final potential ##V_{f}## is going to be: ##V_{1f}=V_{2f}=V_{f}=\frac{q_{1}-\Delta q}{C_{1}}##... that makes sense, right?

gneill
Mentor
Ok, so, since ##V_{1}>V_{2}##, I'll have a ##\Delta q## transferring from 1 to 2, so the final potential ##V_{f}## is going to be: ##V_{1f}=V_{2f}=V_{f}=\frac{q_{1}-\Delta q}{C_{1}}##... that makes sense, right?
Yes. But you're left with two unknowns: ##V_f## and ##\Delta q##. Write the expressions for both of the capacitors and you'll have two equations in those two unknowns.

greg_rack
Gold Member
Yes. But you're left with two unknowns: ##V_f## and ##\Delta q##. Write the expressions for both of the capacitors and you'll have two equations in those two unknowns.
Yep, sure!
Thank you very much :)