Can someone help me with time decay of a capacitor?I have the answers for 3,4, a

Question

Can someone help me with time decay of a capacitor?I have the answers for 3,4, and 5. However, I can't get the right answer for 6. If anyone could be kind enough to help, I would greatly appreciate it!

For 3, the answer is b.

For 4, the answer is b.

For 5, the answer is e.

For 6, the answer should be b.

This question and the next three pertain to the following situation:

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.

What is the current I1 through resistor R1immediately after the switches are closed?

QUESTION 4*

A very long time after the switches are closed, the current I2 is:

(a)   I2 > 0
(b)   I2 = 0
(c)   I2 < 0 (i.e. opposite the direction shown)

QUESTION 5*

What is the charge Q2 on capacitor C2 a very long time after the switches are closed?

(a)   Q2 = 0 ?C
(b)   Q2 = 33 ?C
(c)   Q2 = 90 ?C
(d)   Q2 = 180 ?C
(e)   Q2 = 270 ?C

QUESTION 6**

After a very long time with both switches in the closed position, switch S2is 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 ?sec
(b)   t1/e = 1500 ?sec
(c)   t1/e = 3000 ?sec
(d)   t1/e = 3600 ?sec
(e)   t1/e = 4800 ?sec

Explanation / Answer

C2 and C3 in parallel = 5 * 10E-5 Farads
When S2 is opened this combination will discharge thru R3
The time constant RC = 30 * 5 * 10E-5 = 1.5 * 10E-3 sec
Q / Q0 = .368 = e^-(t / 1.5 * 10E-3)
ln .368 = - t / 1.5 * 10E-3
t = 1.5 * 10E-3 sec = 1500 usec

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