topic Re: Mathcad Community Challenge September 2022 - Resistors in Parallel in Mathcad

Mathcad Community Challenge September 2022 - Resistors in Parallel

DaveMartin — Tue, 04 Feb 2025 21:50:23 GMT

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!

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

Cornel — Thu, 08 Sep 2022 08:25:39 GMT

Hello,

My first try (Mathcad Prime 7):

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

LucMeekes — Thu, 08 Sep 2022 09:14:53 GMT

Here's a solution in Prime 4 express.

Luc

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

Fred_Kohlhepp — Thu, 08 Sep 2022 11:29:59 GMT

Calculating resistance and current for each resistor is simple.

Calculating resistance and current for the network is more pertinent:

Prime Express 4 attached

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

RantEng — Thu, 08 Sep 2022 16:57:40 GMT

I like to use Mathcad symbolics for insights into how to derive solutions. My final and generalized answer for the total resistance equation is:

The complete solution is attached.

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

ppal — Thu, 08 Sep 2022 20:43:37 GMT

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

ttokoro — Fri, 09 Sep 2022 01:51:53 GMT

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

ttokoro — Fri, 09 Sep 2022 02:03:22 GMT

In your Mathcad sheet, you write,

When then the resistance approaches zero.

However, Fred, ppal and others show the total parallel resistance is

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

LucMeekes — Fri, 09 Sep 2022 12:25:03 GMT

Here's another incarnation, using recursion to generate the resistor values:

Prime 4 attached, works also in Prime Express.

Luc

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

ttokoro — Sat, 10 Sep 2022 05:16:57 GMT

Prime 8 with plot.

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

ppal — Sun, 11 Sep 2022 22:29:09 GMT

Just another one.

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

ttokoro — Tue, 13 Sep 2022 05:12:44 GMT

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

ttokoro — Tue, 13 Sep 2022 06:47:40 GMT

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

DJNewman — Tue, 13 Sep 2022 12:17:00 GMT

Hi @ttokoro , would you care to please attach your worksheet? Not just screenshots?

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

RantEng — Tue, 13 Sep 2022 12:22:04 GMT

Good catch. I stand corrected. I was not considering that the the resistors are increasing in value. Before stating so, I should have taken the extra step to derive the limit as you did,

Bob

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

Strib — Fri, 16 Sep 2022 23:58:13 GMT

Some nice analyses, indeed.

But... don't do this at home!

Even just the first 10 ohm resistor is dissipating 4840 Watts, and the others not much less! Gonna get toasty in there!

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

Fred_Kohlhepp — Sat, 17 Sep 2022 12:23:54 GMT

Yeah, don't try this as home, Or anywhere else but as an exercise.

(We could argue that you deserve the burnt fingers and having to sweep up the charred remains, but . . .)

Here's your sign!

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

SC_2975838 — Sat, 17 Sep 2022 13:59:56 GMT

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

SC_2975838 — Sat, 17 Sep 2022 13:58:23 GMT

Re: Mathcad Community Challenge September 2022 - Resistors in Parallel

ttokoro — Mon, 19 Sep 2022 00:39:51 GMT

Solved: Solve diagonal resistance of resistor mesh. - PTC Community

Solved: Solve diagonal resistance of resistor 3D mesh. - PTC Community