Three capacitors RC circuit questions

AI Thread Summary
The discussion revolves around a circuit with three resistors, three capacitors, a battery, and two switches, focusing on the charge on capacitor C2 after closing the switches and the time it takes for the charge to drop after reopening switch S2. For Part A, the correct charge on capacitor C2 after a long time is determined to be 270 μC. In Part B, after switch S2 is reopened, it takes 1500 μsec for the charge on C2 to drop to 1/e of its fully charged value. The participants clarify the circuit's behavior, noting that once S2 is opened, the right side of the circuit becomes isolated from the left side, affecting the analysis of resistors R1 and R3. The discussion emphasizes understanding circuit isolation and time constants in capacitor discharge scenarios.
syhpui2
Messages
23
Reaction score
0

Homework Statement



Three resistors, three capacitors, a battery and two switches are connected in the circuit shown below. The values of all circuit elements are given in the figure. Originally, the switches S1 and S2 are open (as shown) and all of the capacitors are uncharged. At time t = 0, both switches are closed.

http://i.imgur.com/BOq2c.png
BOq2c.png



Part A

What is the charge Q2 on capacitor C2 a very long time after the switches are closed?
(a) Q2 = 0 μC
(b) Q2 = 33 μC
(c) Q2 = 90 μC
(d) Q2 = 180 μC
(e) Q2 = 270 μC (Correct Answer)



Part B

After a very long time with both switches in the closed position, switch S2 is reopened. How long (t1/e) does it take for the charge on capacitor C2 to drop to 1/e (36.8%) of its fully-charged value (i.e. of the value it had just before S2 was reopened)?
(a) t1/e = 1200 μsec
(b) t1/e = 1500 μsec (Correct Answer)
(c) t1/e = 3000 μsec
(d) t1/e = 3600 μsec
(e) t1/e = 4800 μsec



Homework Equations



KVL,KCL

The Attempt at a Solution



For part A, what I tried is
Voltage across is 18 X ¾ (R3/ (R1+R3))= 27/2
(Because Q=CV and in this case Ic=0 so no current on R2?)
I get right answer, just not sure if I am thinking correctly.

For part B,
I used

Q= Q(0)e^-(t/tau)

However, I am not sure how do I find time constant in this case.

THX!
 
Physics news on Phys.org
Your part A method is fine.

For part B, once switch S2 is opened the right hand portion of the circuit is isolated from the left hand portion. So it's just two parallel capacitors and a resistor. What does that suggest to you?
 
gneill said:
Your part A method is fine.

For part B, once switch S2 is opened the right hand portion of the circuit is isolated from the left hand portion. So it's just two parallel capacitors and a resistor. What does that suggest to you?

How about R1 and R3 in this case?
Are they in parallel?
Thanks
 
syhpui2 said:
How about R1 and R3 in this case?
Are they in parallel?
Thanks

No! With switch S2 open they are isolated from each other (no complete circuit).
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
Back
Top