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!

16-Pearl

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Mathcad Community Challenge September 2022 - Resistors in Parallel

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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:

Resistors Challenge.png

Find the Mathcad Community Challenge Guidelines here!

C

Cornel

19-Tanzanite

Hello,

My first try (Mathcad Prime 7):

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1_Mathcad_Challenge_September_2022_Resistors_in_Parallel.zip

2_Mathcad_Challenge_September_2022_Resistors_in_Parallel.pdf

L

LucMeekes

23-Emerald V

Here's a solution in Prime 4 express.

Luc

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1_LM_20220908_Resistors-in-parallel.zip

F

Fred_Kohlhepp

23-Emerald I

Calculating resistance and current for each resistor is simple.

Calculating resistance and current for the network is more pertinent:

Prime Express 4 attached

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1_MC-challenge-9_2022.zip

RantEng

14-Alexandrite

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.

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Robert (Bob) Adams

1_Rresistors-in-Series.zip

ttokoro

21-Topaz I

In your Mathcad sheet, you write,

When then the resistance approaches zero.

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

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t.t.

RantEng

14-Alexandrite

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

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Robert (Bob) Adams

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ppal_255687