Kirchhoff's Law - Differential Equation

Reuel · 2011-02-01 15:10:26

I have never taken physics and I do not understand what the question is asking.

"Kirchoff's Law states that a simple circuit containing a resistor of R ohms and an inductor of L Henrys in series with a source of electromotive force that supplies a voltage E(t) volts at time t satisfies

where I is the current measured in amperes.

Consider a circuit with L = 6 Henrys, R = 6 ohms, and a battery supplying a constant 12 volts. If I = 0 at t = 0, find I at time t."

I have no idea what most of that means. Do I need to understand physics to be able to solve the problem? Or is it like that raindrop problem from a week or so back that implies physics but does not require a knowledge of it?

Thanks!

Last edited by Reuel (2011-02-02 01:08:44)

bobbym · 2011-02-01 15:17:25

Hi Reuel;

You will not need any electronics knowledge to solve the problem. When in that form it is a math problem. Just solve the DE.

Reuel · 2011-02-02 00:21:18

Okay, well, a couple of questions. First, do you enter all of the values for the constants before or after the differential equation has been solved? Second, there are two functions of time: amperes, I(t), and the electromotive force that provides voltage 12.

Here is my effort in setting it up in a way I think may be best. Is this in the right direction or am I mistaken?

Solving for the conditions given,

Is that the end of the problem? I am not sure what is meant by "find I and t" if it means more than finding I as a function of t.

Thanks.

bobbym · 2011-02-02 00:44:59

Hi Reule;

That is what I have too. I used separation of variables though. I think the problem is done

Bob · 2011-02-02 00:49:32

hi Reule,

Me too. I think the last words should be "find I at time t".

Next bit under review while I consult a scientist.

Aarhh I think I get it. Apologies to any physicists reading this. The inductor offers reistance to the currect of electricity flowing through it. At the start t = 0 so I = 0. No change of current. As time passes the inductor stores energy. (Think of it as being like rolling a rock up a hill. When you stop rolling you still have to hold the rock against tumbling down again.) As t tends to infinity (like I'm slowing down my rate of assent) all that is needed is to overcome the resistor and that (by ohms law) leads to a current of 2 amps. But it must be maintained or the inductor lets go its stored energy. So your equation describes this perfectly. Hurrah for mathematicians!

Bob

Last edited by Bob (2011-02-02 01:15:13)

Reuel · 2011-02-02 01:06:28

bobbmy - Thanks for your help! I have a few other "tricky" problems I'll post but I think I am getting the hang of it. I am still trying to learn Newton's Law of Cooling, which I have a couple of specific examples to use.

bob - ahhh... Yes, at time t. My instructor does make a lot of typos. This was just a suggested practice sheet - the worst is when they appear on exams. And thanks, too, for the physics explanation! That puts it into context.

Bob · 2011-02-02 01:16:03

watch out I've amended what I posted just now!

Bob

Reuel · 2011-02-02 01:19:10

I caught it. Thanks so much.

bobbym · 2011-02-02 01:26:01

Hi Reuel;

Just post what you have along with the work. I would say that you are getting it.

Math Is Fun Forum

#1 2011-02-01 15:10:26

Kirchhoff's Law - Differential Equation

#2 2011-02-01 15:17:25

Re: Kirchhoff's Law - Differential Equation

#3 2011-02-02 00:21:18

Re: Kirchhoff's Law - Differential Equation

#4 2011-02-02 00:44:59

Re: Kirchhoff's Law - Differential Equation

#5 2011-02-02 00:49:32

Re: Kirchhoff's Law - Differential Equation

#6 2011-02-02 01:06:28

Re: Kirchhoff's Law - Differential Equation

#7 2011-02-02 01:16:03

Re: Kirchhoff's Law - Differential Equation

#8 2011-02-02 01:19:10

Re: Kirchhoff's Law - Differential Equation

#9 2011-02-02 01:26:01

Re: Kirchhoff's Law - Differential Equation

Board footer