An uncharged capacitor and a resistor are connected in series to a source of emf

Question

An uncharged capacitor and a resistor are connected in series to a source of emf. If E = 9.00 V, C = 20.0 F, and R = 100 , find (a) the time constant of the circuit, (b) the maximum charge on the capacitor, and (c) the charge on the capacitor after one time constant.

For part A I got the following answers:

a=2000T b=180uC c=113.78

PART B

Consider the second problem above. After 3 time constants (3) has passed the charge on the capacitor is _______ compared to the maximum possible charge on the capacitor.

Question 2 options:

equal in magnitude

greater than 90%

between 50% and 70%

unrelated to

between 70% and 90%

less than 50%

For part be, I got the charge to be 0.29uC. But I'm don't know if that is correct, and how to figure out the percentage.

equal in magnitude

greater than 90%

between 50% and 70%

unrelated to

between 70% and 90%

less than 50%

Explanation / Answer

Part A,
Time Constant, t = R*C
t = 100 * 20 uF
t = 2000 u s
t = 2 * 10^-3 s

Maximum Charge, Q = C* v
Q = 20.0 * 9
Q =180 uC

q = Q(1 - e^-(t/RC))
After 1 time constant,
q = 180 uC * (1 - e^-1)
q = 113.78 uC

After 3 time constant,
q = 180 uC * (1 - e^-3)
q = 171.0 uC

171.0/180 * 100% = 95 %

So the correct option is (b) Greater than 90%

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