RC Circuit , Calculate Time Constant

[ParoXsitiC]

Homework Statement

Given this diagram:

Picture mirror: http://i.minus.com/1331507225/3XjEXOAlTaoJBoBuQFoJiQ/itFBvAiitDZQc.png

With S1 switch closed and S2 switch left open, I am trying to find the time constant

Homework Equations

I know τ = RC for a basic circuit, but how would you calculate it for a complex circuit? Is R the equivalent resistance to the battery?

Q=VC
V=IR

i = dq/dt
dq/dt + Q/τ - emf / R = 0

The Attempt at a Solution

I start with junction rule and loop rule

I1 = I2 + I3
-emf + I1R1 + Q/C + I2R2 = 0
=emf + I1R1 + I3R3 + I3R4 = 0

At this point the teacher says I2 = dq/dt and we need to get rid of I1 so we can put something next to the C in Q/C.

I use I1 = I2+I3 in junction rule and put it into loop rule #2, getting:

-emf + (I2 + I3)R1 + I3R3 + I3R4 = 0
I2R1 + I3(R1+R3+R4) = emf
I3 = (emf - I2R1) / (R1+R3+R3)

Then I put I3 in for the I1 eq.

I1 = I2 + (emf - I2R1) / (R1+R3+R3)

At this point it's so messy and confusing I think I am doing it all wrong.

The baseline she is giving us is that

dq/dt + Q/[foo] - emf/[bar] = 0

where [foo] would be the time constant. In a simple circuit she gives [foo] = RC and [bar] = R

 

[ehild]

I do not see any diagram... ehild

 

[ParoXsitiC]

I do not see any diagram...


ehild

Weird, it's possible minus.com isn't showing up for you. I will upload it