Is this correct?

Qualitatively that is correct.
But I would assume they want the exact calculated time to within 95% of the final value.
Do you know how do do that from the equation for the circuit transient response?

 

Qualitatively that is correct.
But I would assume they want the exact calculated time to within 95% of the final value.
Do you know how do do that from the equation for the circuit transient response?

I'm afraid not.

 

I'll check that out. I also noticed that on another thread you recommended a book called Analog filter design? I'm assuming this could be useful for me as well. Do you have any other recommendations?

As for those relationships you mentioned, are you talking about Ohms law?

Van Valkenburg, M.E., Analog Filter Design, (1982) or
Schaumann, R., & Van Valkenburg, M.E., Analog Filter Design, (2001), are separate editions of the same book. They are advanced undergraduate to graduate level textbooks. They may be unsuitable for you if you do not have a good knowledge of complex analysis and Laplace Transforms. The developments are heavy and some details are missing because it is assumed that the reader has the requisite background to fill them in. I myself found them "dense" in places.

Yes Ohms Law, but extended to allow for complex impedance:

1. For a resistor ZR = R + j0
2. For a capacitor ZC = 0 + 1/(jωC)
3. For an inductor ZL = 0 + jωL

 

"But I would assume they want the exact calculated time to within 95% of the final value.
Do you know how do do that from the equation for the circuit transient response? "

Can I do it using the following equations?

Q = CV (C here is the value of the capacitor?)
τ = R x C
Vs - R x i(t) - Vc(t) = 0

 

Can I do it using the following equations?

Q = CV (C here is the value of the capacitor?)
τ = R x C
Vs - R x i(t) - Vc(t) = 0

Almost, but what you actually need is the solution to the first order differential equation that represents the RC circuit with appropriate initial conditions. It involves an exponential function which follows intuitively from the realization that it is one of the few functions where it is possible to combine a function with its derivative by addition. That is the same as saying that the function and its derivative have the same functional form.

Check out the following article:
https://en.wikipedia.org/wiki/RC_circuit