Mathcad Community Challenge September 2022 - Resistors in Parallel

[DaveMartin]

This month’s challenge is related to electrical engineering. We have a simple circuit with an electrical potential of 220 Volts. Initially we have a single 10 Ohm resistor. Then we add a second resistor in parallel, with 10% higher resistance. Then we add a third resistor in parallel, with 10% higher resistance than the previous resistor. And so on.

• Calculate the current in the circuit for the single resistor case.
• Calculate the resistance of each additional resistor and current through each resistor for 2, 3, 4, 5, and 10 resistors in parallel.
• Can you write a function or program that calculates the resistance of each resistor and current through each resistor for n resistors in parallel?

These calculations are fairly straightforward, so it will be interesting to see what tools – vectors, matrices, loops, plots, charts, etc. – that you use to solve the problem. As always, how you document your calculations is important as your worksheet will be visible to the community.

Here is an example of three resistors in parallel, as drawn in Creo Schematics:

Find the Mathcad Community Challenge Guidelines here!

[DJNewman]

I hope Dave can handle going through the volume of people getting into the challenge this time! I'm looking forward to what he has to say about the contributions.

September ends after tomorrow, so if you're still thinking about submitting something, now's the time!

[DaveMartin]

Ha ha, I was thinking about that myself. I had no idea this challenge would be so popular. I've got my work cut out for me this weekend. I'll be reviewing all submissions while watching football. Speaking of which, I have an idea for a football-related geometry problem for November. So football fans, stay tuned...

[Strib]

Hi Dave,

Yes, you generated a lot of interesting responses!

I hope you like my simple closed-form expression for the solution – that didn’t even use Mathcad. No offense intended in doing that – have used MCD for EE work since its DOS version.

Strib

[DJNewman]

https://www.mathcad.com/en/blogs/community-challenge-resistors-in-parallel

Sorry for it taking so long to get the solutions blog up. That's on PTC, not on Dave.

But everyone who participated here got the PTC Community badge for doing so, and a mention on the Mathcad.com blog! Hope y'all had fun! And we hope others can learn from what was done here.