Hello again,

What else people do is use plus and minus symbols (+) and (-) for the voltages if you like that better.

I left the arrow across the cap out because it was curved so it was a little unclear. I was going to redraw it straight but then must have forgotten. So you can put that back if you like. I made a new drawing also showing the plus and minus symbols for clarity.

It's good to be clear because then other people understand what you are doing better.

 

I've been at this thing for some hours now. Finally I've come up with this... it seems to work out at least mathematically but I feel as if I've cheated and not used the proper rules of transposition. I'm going to work on the calculus later... provided it ok and correct. What do you think? It feels like a victory of sorts... but somehow empty.

 

Hello again,

That's getting much better.

It's close, but notice your fourth equation does not come from the third equation because when you multiply both sides of the 3rd one by R1*R2 you dont get the 4th one, and that is because we get an R1 and R2 on the left in the numerators also, multiplied by v, but the 4th equation doesnt have that.

That is just algebra up to this point.

Also note that with that approach to solving the DE i think it may be difficult so it would probably be better to use the integrating factor form. You can do it that way for comparison though, but you may find a snag that you might not like to have to figure out how to handle. By all means though if you feel like it then try it both ways.

 

I spent hours with it last night MrAI. I can upload the pics if you want but its a jumble of madness. Could you show me, how you would do it? I think I'm missing a trick that I need to learn, to solve it properly. I've compressed it expanded it, factored it, multiplied across it, you name it. In the end I solved this by assigning it values, which is why I said it works mathematically.

 

I spent hours with it last night MrAI. I can upload the pics if you want but its a jumble of madness. Could you show me, how you would do it? I think I'm missing a trick that I need to learn, to solve it properly. I've compressed it expanded it, factored it, multiplied across it, you name it. In the end I solved this by assigning it values, which is why I said it works mathematically.

Hi again,

Ok no problem.

Starting from your equation:
(E-v)/R1-v/R2=C*dv/dt

expanding:
E/R1-v/R1-v/R2=C*dv/dt

If we multiply both sides by R1 we get:
E-v-v*R1/R2=R1*C*dv/dt

and now multiply both sides by R2 we get:
E*R2-v*R2-v*R1=R1*R2*C*dv/dt

and you can see we get something slightly different here.
[note we 'could' use integrating factor next but we dont yet]
Next divide both sides by the left hand side, then divide both sides by R1*R2*C and get:
1/(C*R1*R2)=(dv/dt)/(E*R2-v*(R2+R1))

then multiply both sides by dt and get:
dt/(C*R1*R2)=dv/(E*R2-v*(R2+R1))

and now we have everything with 't' on the left and everything with 'v' on the right.
This is ready for integration, but it may not be easy to accomplish the right side integration depending on what you did in this area in the past. I use automatic software these days unless it cant handle the integration. You could try that if you like, or use another method.

See if this makes sense so far. Once you get to that point we can move to solving it completely.

Dont get bothered if you cant do something right away. In education some things we can figure out but other things we have to be told. There are maybe only a few people who could figure out Special Relativity if they were never told about it first.

 

Nope lol...You lost me at step 5 there, but don't worry about it.

I'm a second year MrAI, tbh I'm struggling with the level I'm at; at the moment... This stuff is even a step beyond that again... I'm going to return to this over the summer, as I suspect this is coming for me next year!

Let me show you the level of questions, we're doing at the moment. I'm going to start to run into problems between number 7 - 12 of the attached file. Also question 2.

 

Hello again,

Well starting with:
E*R2-v*R2-v*R1=R1*R2*C*(dv/dt)

divide both sides by the left hand side we get:
1=R1*R2*C*(dv/dt)/(E*R2-v*R2-v*R1)

That makes sense right?

Then just divide both sides by R1*R2*C and get:
1/(R1*R2*C)=(dv/dt)/(E*R2-v*R2-v*R1)

Did you have much algebra in the past?

 

Hello again,

Well starting with:
E*R2-v*R2-v*R1=R1*R2*C*(dv/dt)

divide both sides by the left hand side we get:
1=R1*R2*C*(dv/dt)/(E*R2-v*R2-v*R1)

That makes sense right?

Then just divide both sides by R1*R2*C and get:
1/(R1*R2*C)=(dv/dt)/(E*R2-v*R2-v*R1)

Did you have much algebra in the past?

Hello again,

I was just wondering if that made sense to you?
If not, we can back up a little no problem.

 

Ah yes... now I see. Sorry I was like a zombie there for a few days. Couldn't get my head round the math. Sleep deprivation + math = 0 ts where ts is = to test score...
I have one coming up now in power transmission fault finding. All my efforts being going into this module we've been working on so the next few days are going to transmission. Let' take a little break from this for a while if we could. I got 2 crappy test scores this week and I really don't want a third for next week. Thank you for taking the time to work on this with me. I think I would have completely failed it without you.

 

Hi,

Well thanks, and yes when you get back we can do more. Just remind me what we were doing then

Here is a full workup of the problem, one way to do it.
Note the software separates the exponents in the powers of e so just combine them if you like.

The form for the integration is 1/(K-v) with K a constant and v the voltage as before.
Here is the workup, but still i think it would be better to use the integrating factor solution.