# Circuits Problem Solution

This problem was sent to me recently. I have made some additions to the graphic.

On every time step of a numerical solution, I do the following:

1) Update the capacitor voltage based on the capacitor current from the previous time step
2) Solve for the voltage at point B based on the nodal equations at point C.
3) Solve for the capacitor current

Assume that point C is the reference voltage point, with zero voltage. Let $V_C$ denote the voltage across the capacitor. The node equation at point C is:

$\frac{0 - V_B}{R} + \frac{0 - (V_B + V_C - V)}{2 R} + \frac{0 + 2V - (V_B + V_C)}{R} = 0$

Note that $V_A = V_B + V_C - V$. Solve the above equation for $V_B$. Then find the current through the capacitor as follows:

$V_A = V_B + V_C - V \\ I_C = \frac{V_B - V_A}{R} + \frac{V_B - 0}{R}$

Simulation code below. Results are printed at the end of the code.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 import math # Constants R = 1.0 C = 10.0**(-6.0) V = 8.0 us = 10.0**(-6.0) dt = 10.0**(-10.0) ################################ # Initialize simulation VC = 0.0 right = (VC - V)/(2.0*R) - 2.0*V/R + VC/R left = -2.0/R - 1.0/(2.0*R) VB = right/left VA = VB + VC - V IC = (VB-VA)/R + VB/R VCd = IC/C ################################ # Run simulation t = 0.0 while t <= (5.0/8.0)*us: VC = VC + VCd*dt right = (VC - V)/(2.0*R) - 2.0*V/R + VC/R left = -2.0/R - 1.0/(2.0*R) VB = right/left VA = VB + VC - V IC = (VB-VA)/R + VB/R VCd = IC/C t = t + dt ################################ print dt print t print "" print IC print VA #>>> #1e-08 #6.3e-07 #5.79176835692 #2.55205791077 #>>> ================================ RESTART ================================ #>>> #1e-09 #6.25e-07 #5.88135906014 #2.52966023496 #>>> ================================ RESTART ================================ #>>> #1e-10 #6.25e-07 #5.88560014166 #2.52859996458 #>>> 

Note by Steven Chase
11 months ago

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@Steven Chase Thanks for the solution.

@Steven Chase can we solve this using pen and page only??

I would like to see the official solution. The numerical solution seems much more natural to me, as usual. I also think it is interesting that they are asking for approximations.

- 11 months ago

@Steven Chase the official solution is not available in website , in that image you can see it is written NA which means not available.
I will say my physics teacher to upload the solutions now.

Is this your schoolwork or a problem from a university textbook?

- 11 months ago

If this is your schoolwork, I must say your school is quite hard.

- 11 months ago

@Krishna Karthik this is work of a problem like of JEE.
But it is not in our school course .
I have separately joined a Institute (coaching) for JEE preparation.

Ah. that explains it. Holy shit... JEE's hard. Lol I live in Australia so I can't try JEE. I'm doing IB physics Higher Level; it's sort of in-between JEE and AP Physics.

Bro, you'll definitely get into IIT though. You're already way ahead lol

- 11 months ago

@Krishna Karthik i can give jee advance papers. Do you want to try those problems.??
I have jee level millions of problems.

Sure! Thank you so much bro. But only classical mechanics. I haven't started on Electromagnetism yet lol

- 11 months ago

@Krishna Karthik no problem. I have separate practice problem for each topic. . But the condition is you have to use ony Pen and page.

Yes; of course. I'll try my best. Beautiful!

- 11 months ago

It'll be amazing practice for my physics exams.

- 11 months ago

Did you try my new problem btw? I have to see if my solution's right...

- 11 months ago

@Krishna Karthik did you have studied Thermodynamics??

No, not yet. I am working mostly on my maths and computer science; physics is kind of my side thing that I teach myself on brilliant.

This is because I haven't formally started physics in school yet.

I have started on Special Relativity though lol. It's easier than thermodynamics for sure, but I might start on it soon.

- 11 months ago

@Krishna Karthik so basically you want mechanics. I am giving you 27 problems.
2-3 are not in mechanics you can neglect them .

Thanks! Epic bro.

- 11 months ago

@Krishna Karthik Brilliant is not accepting PDF. Let me you 4-5 photos.

You can upload the photos onto a discussion. Photos are fine. Thx mate!

- 11 months ago

In the first page (in our school, we have been taught that you don't have to derive left in every question)
But for explaining I have derived for you.
My friends always follow school teachers and use this method and I always solve differential equation for this problems .
What do you think which method is best ?
BTW the official solution are not yet uploaded in the website, I solved 1st problem myself and here is the solution below.

Generally speaking, differential equations and ground-up mathematics is the correct way to do physics. But for high-school or on a test it'll take time to derive, so I just use formulas for high-school.

- 11 months ago

And literally all laws in physics are written in the form of ODEs and PDEs, so high-school just uses approximations or makes some values constant so that rates of change and calculus doesn't have to be used. For obvious reasons as not everyone is a maths wiz.

- 11 months ago

@Steven Chase sir did you have seen this type of method.

That's kind of a nice approach. It just depends on what tools you're allowed to use

- 11 months ago

By the way, I'm planning to make a time-domain version of your maximum power transfer problem, if that's OK with you

- 11 months ago

@Steven Chase did you have woke up now??

@Steven Chase why not sir? It will be interesting.

Thx! Cheers

- 11 months ago

@Krishna Karthik you can print it out. It will be helpful.

@Steven Chase is it uploaded now??

Yes, it is

- 11 months ago

Hmmm... I wonder... Why has Neeraj Anand Badhgujar deleted his account?

- 11 months ago

There was a bit of drama earlier that I won't describe in detail. I don't think he needed to delete his account though.

- 11 months ago

What happened though? He was a friend. I hope you won't mind telling me... it's alright if you won't though... thanks

- 11 months ago

@Steven Chase I am getting these 2 equations
x and y are charges And Wolfram has failed to solve and I don't think I can solve this with laplace.
So I am planning to use python
But I didn't know how to use python for this work. Can you please little bit guide me?

On every time step, you can do:

 1 2 3 4 5 6 x = x + xd*dt y = y + yd*dt xd = xd + xdd*dt yd = yd + ydd*dt xdd = (insert expression here) ydd = (insert expression here) 

- 11 months ago

That is just a general format. You can modify as necessary

- 11 months ago