The circuit in the figure has a capacitor connected to a battery, two switches,

Question

The circuit in the figure has a capacitor connected to a battery, two switches, and three resistors. Initially, the capacitor is uncharged and both of the switches are open.
(a) Switch S1 is closed. What is the current flowing out of the battery immediately after switch S1 is closed?
1

(b) After about 10 min, switch S2 is closed. What is the current flowing out of the battery immediately after switch S2 is closed?
2

(c) What is the current flowing out of the battery about 10 min after switch S2 has been closed?
3

(d) After another 10 min, switch S1 is opened. How long will it take until the current in the 200- resistor is below 1 mA?

Explanation / Answer

a)

i = V/R = 6/400 = 0.015 A

------------------------------------

b)

R = 300+(200/3) = 366.667 ohm

i = V/R = 6/366.667 = 0.01636A

-----------------------------------

c)

i = V/R = 6/400 = 0.015 A

----------------------------------

d)
= RC = 300*0.004 = 1.2

i0 = 6/300 = 0.02

i = i0 * e^(-t/) >>>> 0.001 = 0.02 * e^(-t/1.2)

>>>>> e^(-t/1.2) = 0.05

>>>> t = 3.59 s

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