Calculating Potential Difference in a Capacitor with Resistors Circuit

[NWNINA]

Homework Statement

In the following circuit, the ideal battery has an electromotro force of 12V, the resistances R1=4 ohms and R2 = 6 ohms. The capacito of 6x10^-6 F can be found discharged initially. The switch closes at t=0. Calculate the potential difference in the capacitor when t=2$\tau$

Homework Equations

q=q_o e^(-t/RC)

$\tau$ =RC

The Attempt at a Solution

I have tried many things, but nothing seems to be working.

 

[NascentOxygen]

Hi NWNINA! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

What have you tried? Show your working.

 

[NWNINA]

Hi NWNINA! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

What have you tried? Show your working.

this is one of the things i tried:

Vo = (12V/10) * 6 = 7.2V

V=(7.2V)*e^(-2t/t)=.97V

ΔV=6.23V

 

[NascentOxygen]

If R1 were zero ohms, after the switch is closed what would be the final voltage across the capacitor? Trace the full path of current as it leaves the battery and charges the capacitor.

 

[theBEAST]

If R1 were zero ohms, after the switch is closed what would be the final voltage across the capacitor? Trace the full path of current as it leaves the battery and charges the capacitor.

I would like to know how to do this question as well. So I found the current using I=I_o*e^(-2t/t) and then I used V=IR to solve for the potential difference. Am I on the right track? If I am what would I use for R, the total resistance of the circuit or just the 4ohm resistor?

 

[Rayquesto]

how would you find Potential Difference when a charge exists in a capacitor? Also, I believe that equation for charge after some time in the capacitor is too general. You must consider the initial charge in the emf and then take a special difference. The equation is derived from a differential equation that looks like this: q(t)=Q0(1-e^-t/RC)

 

[NascentOxygen]

I would like to know how to do this question as well. So I found the current using I=I_o*e^(-2t/t) and then I used V=IR to solve for the potential difference. Am I on the right track? If I am what would I use for R, the total resistance of the circuit or just the 4ohm resistor?

Can you trace the closed-loop path that current would be taking?