You are here:

# Electronics/circuit question

Question

image of page
Hi,

I have a simple example from my physics text using a separable ODE, but I don't understand the steps that they took to solve it.  It should be pretty straightforward, but I am getting something different when I try to solve.  I've attached the image of the page where my questions are, and a red "1" and "2" indicates my problems with it.

Note:  C = capacitor, E = emf of battery, q = charge in circuit

#1:  I don't understand how they got the final answer here.  If you multiply (CE - q)/RC by -1, you'd get (q-CE)/RC.  So how did they get -(q-CE)/RC ?  Seems like there's an extra negative sign.

#2:  I don't understand the integral solved on the left side of int((dq/(q-CE)) to get what they have for ln((q-CE)/(-C)).

I would have thought that int((dq/(q-CE)) = ln(q-CE)

I know these seem simple, but an I missing something obvious here in these?

In red 1, CE-q numerator, they just pulled out the "-" and made it -(-CE+q) = -(CE-q).

In #2, same type of arithmetic, just manipulate the equation without changing its quantity; remember you can do the same thing to each side of an equation and it doesn't effect the result.

Hope this helps.

Electronics

Volunteer

#### ZZ

##### Expertise

Electronics questions about AC, DC and digital theory.

##### Experience

Graduate electrical engineer with over 40 years in electronic design, manufacturing, project organization and patent review. Experience in fields of industrial and consumer electronics (audio, video, acoustics, etc.)

Organizations
IEEE (Institute of Electrical and Electronics Engineers); Senior Life member AES (Audio Engineering Society), Fellow Life member

Education/Credentials
BSEE University of North Dakota