How Do You Prove and Analyze RC Circuit Formulas?

[dmitriylm]

Homework Statement

I'm doing a physics lab and have a question about RC circuits. I'm given four formulas:

1a) dQ/dt = -Q/RC
1b) Q = (Qo)e^(-t/RC)
1c) E - RI - Q/C = 0 ---> R(dQ/dt) + Q/C - E = 0
1d) Q(t) = CE[1 - e^(-t/RC)]

I am told that 1b is the solution to 1a and 1d is the solution to 1c.

a) Equation 1b is called "the solution" to the differential question, 1a because when you plug in Q(t) (from 1b) into equation 1a, the resulting left side of the equation is equal to the right side. Prove that 1b is the solution by plugging it into equation 1a.

b) Demonstrate that RC has the dimensions of time.

c) Plug 1d into 1c and show that it works, as you did in question a.

d) Differentiate Q(t) to obtain an expression for the current.

Homework Equations

1a) dQ/dt = -Q/RC
1b) Q = (Qo)e^(-t/RC)
1c) E - RI - Q/C = 0 ---> R(dQ/dt) + Q/C - E = 0
1d) Q(t) = CE[1 - e^(-t/RC)]

The Attempt at a Solution

Not quite sure what should be done to make this work. Can anyone please explain this for me?

 

[lewando]

This is really more of an Introductory Physics type question.

a) they are telling you exactly how to proceed--plug eq. 1b into eq. 1a. (you'll need to be able to differentiate eq. 1b with respect to time).
b) you are being asked to do a dimensional analysis of RC. Hint: R and C are SI "derived units" (based on SI "base units").
c) same as a)
d) you'll need to differentiate eq. 1d with respect to time, which you already did if you did part c).