Three capacitors RC circuit questions

In summary, a circuit with three resistors, three capacitors, a battery and two switches is described. The values of all circuit elements are given. At time t=0, switches S1 and S2 are closed, causing all capacitors to become uncharged. Part A asks for the charge on capacitor C2 after a very long time, with the correct answer being Q2=270 μC. Part B asks for the time it takes for the charge on C2 to drop to 1/e of its fully-charged value after switch S2 is reopened, with the correct answer being t1/e=1500 μsec. The equations used are KVL and KCL. For part A, the voltage across R2
  • #1
syhpui2
28
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!
 
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  • #2
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?
 
  • #3
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
 
  • #4
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).
 
  • #5


Dear student,

For part A, your approach is correct. Since there is no current flowing through R2, the voltage across it will be 0 and therefore the charge on C2 will be 0. This is because the capacitor acts as an open circuit when it is fully charged.

For part B, the time constant can be found using the formula tau = RC. In this case, R is the equivalent resistance of the circuit, which can be found by combining the resistors in parallel and series. Once you have the value of R, you can use it to calculate the time constant and then solve for t using the given percentage value (1/e).

Hope this helps.
 

1. How do you calculate the total capacitance of a Three Capacitors RC circuit?

To calculate the total capacitance of a Three Capacitors RC circuit, you need to use the formula:
C = C1 + C2 + C3
where C1, C2, and C3 are the individual capacitances of the three capacitors in the circuit. This formula only applies when the capacitors are connected in parallel. If they are connected in series, the total capacitance can be calculated using the formula:
1/C = 1/C1 + 1/C2 + 1/C3

2. How do you find the equivalent resistance of a Three Capacitors RC circuit?

The equivalent resistance of a Three Capacitors RC circuit can be calculated using the formula:
R = R1 + R2 + R3
where R1, R2, and R3 are the individual resistances of the three resistors in the circuit. This formula only applies when the resistors are connected in series. If they are connected in parallel, the equivalent resistance can be calculated using the formula:
1/R = 1/R1 + 1/R2 + 1/R3

3. What is the time constant of a Three Capacitors RC circuit?

The time constant of a Three Capacitors RC circuit is the amount of time it takes for the voltage across the capacitors to reach 63.2% of its maximum value. It is calculated using the formula:
τ = RC
where R is the equivalent resistance of the circuit and C is the total capacitance.

4. What is the charge on each capacitor in a Three Capacitors RC circuit?

The charge on each capacitor in a Three Capacitors RC circuit can be calculated using the formula:
Q = CV
where C is the capacitance of the capacitor and V is the voltage across it. The voltage across each capacitor will vary depending on the circuit configuration and the charge on each capacitor will also change as the capacitor charges and discharges.

5. How do you calculate the voltage across each capacitor in a Three Capacitors RC circuit?

The voltage across each capacitor in a Three Capacitors RC circuit can be calculated using the formula:
V = Q/C
where Q is the charge on the capacitor and C is the capacitance. The voltage across each capacitor will vary depending on the circuit configuration and the charge on each capacitor will also change as the capacitor charges and discharges.

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