Two Loop RC Circuit

1. Mar 17, 2013

fmd826

1. The problem statement, all variables and given/known data

A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 52 Ω, R3 = 41 Ω and R4 = 129 Ω. The capacitance is C = 62 μF and the battery voltage is V = 24 V.

1) The switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?

2) What is I1(∞), the magnitude of the current that flows through the resistor R1 a very long time after the switch has been closed?

3) What is Q(∞), the charge on the capacitor after the switch has been closed for a very long time?

4) Consider the circuit above, with R5 = 119 Ω in series with the capacitor. Once again, the switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?

5) Continuing with the new circuit, what is Q(∞), the charge on the capacitor after the switch has been closed for a very long time?

2. Relevant equations

I=v/r
qmax=C*Vbattery
Q(t)= Qmax(1-e^(-t/T))

3. The attempt at a solution

I have no clue how to do this problem after trying the first few questions. For example I tried the first question and I know after the switch closes, the capacitor acts as a wire, so its just like a circuit with only resistors. I used the equation i=v/r and it didnt work. I tried adding the resistors in different ways but it still didnt work. any help would be awesome. thanks guys!

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Last edited by a moderator: Mar 17, 2013
2. Mar 17, 2013

tiny-tim

welcome to pf!

hi fmd826! welcome to pf!
show us how you added the resistors

3. Mar 17, 2013

fmd826

well resistors in series are added R1 +R2 +R3 etc... i added them all together and then even tried just the inner loop. I know that the current divides at the wire with the resistor. I tried making equations using the loop rule, but theres so many unknowns that I dont think that is the right way to go about this.

4. Mar 17, 2013

fmd826

so the homework program I am using wasnt taking my answer because of the lack of sigfigs. -_-

5. Mar 18, 2013

tiny-tim

hi fmd826!

(just got up :zzz:)
ah, but the right-hand loop aren't in series with the emf …

use the parallel formula to make that loop into one resistor, then put that in series with the emf in the left-hand loop

6. Jul 12, 2015

ayajek

I am trying to solve part 2 of this question. I know that after a very long time the current decreases, but it is not zero in this case. I used kirchoff's rules but since Q1, I1, I3 are unknown, I'm clueless on how to find I1 after a very long time..

7. Jul 13, 2015

Nathanael

After a very long time the capacitor will be charged. If the capacitor is fully charged, what do you think the current through the middle branch will be?

Edit:
I just noticed this is a 2 year old thread. You should make a new thread if you have questions.

Last edited: Jul 13, 2015
8. Jul 13, 2015

Staff: Mentor

It's not clear from the problem statement what circuit is associated with parts 1 through 3. The statement mentions four resistors but the only diagram included shows five and appears to be associated with the "new" circuit of parts 4 & 5. Please clarify the circuit configuration for parts 1 through 3.