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.
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Top Newest@Steven Chase Thanks for the solution.
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@Steven Chase can we solve this using pen and page only??
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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.
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@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.
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@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.
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Bro, you'll definitely get into IIT though. You're already way ahead lol
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@Krishna Karthik i can give jee advance papers. Do you want to try those problems.??
I have jee level millions of problems.
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@Krishna Karthik no problem. I have separate practice problem for each topic. . But the condition is you have to use ony Pen and page.
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@Krishna Karthik did you have studied Thermodynamics??
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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.
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@Krishna Karthik so basically you want mechanics. I am giving you 27 problems.
23 are not in mechanics you can neglect them .
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@Krishna Karthik Brilliant is not accepting PDF. Let me you 45 photos.
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@Steven Chase sir the hand made solution is ready.
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.
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Generally speaking, differential equations and groundup mathematics is the correct way to do physics. But for highschool or on a test it'll take time to derive, so I just use formulas for highschool.
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And literally all laws in physics are written in the form of ODEs and PDEs, so highschool 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.
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@Steven Chase
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@Steven Chase sir did you have seen this type of method.
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That's kind of a nice approach. It just depends on what tools you're allowed to use
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By the way, I'm planning to make a timedomain version of your maximum power transfer problem, if that's OK with you
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@Steven Chase did you have woke up now??
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@Steven Chase why not sir? It will be interesting.
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@Krishna Karthik
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Thx! Cheers
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@Krishna Karthik you can print it out. It will be helpful.
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@Steven Chase is it uploaded now??
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Yes, it is
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Hmmm... I wonder... Why has Neeraj Anand Badhgujar deleted his account?
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@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?
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On every time step, you can do:
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That is just a general format. You can modify as necessary
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Thanks, but how to solve this differential equations??
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