Resistance in Parallel Equation

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Discussion Overview

The discussion revolves around the formula for calculating total resistance in a parallel circuit, specifically comparing the traditional expression 1/R = 1/R1 + 1/R2 + 1/R3 with the alternative form R = 1/(1/R1 + 1/R2 + 1/R3). Participants explore the reasons behind the common usage of the first form and the implications of using the second form.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions why the alternative form R = 1/(1/R1 + 1/R2 + 1/R3) is not commonly used, suggesting it might be easier.
  • Another participant argues that the choice of which form to use depends on the context and what information is available, emphasizing that the 1/R expression is easier to understand and remember.
  • A different participant asserts that the alternative form is indeed used frequently and draws a parallel to how Newton's second law is typically presented, despite the existence of equivalent forms.
  • One participant expresses agreement with the idea that the traditional form makes sense as the standard representation.
  • Another participant reiterates that both equations are mathematically equivalent and suggests that the second form may actually be used more often.

Areas of Agreement / Disagreement

Participants express differing views on the usage and preference of the two forms of the resistance equation. While some acknowledge the traditional form's prevalence, others argue for the validity and utility of the alternative form. No consensus is reached regarding which form is superior or more appropriate.

Contextual Notes

Participants do not delve into specific assumptions or limitations of the equations discussed, nor do they clarify the contexts in which one form might be preferred over the other.

CheesyPeeps
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The formula to find the total resistance in a parallel circuit is 1/R=1/R1+1/R2+1/R3, but wouldn't it be easier to use R=1/(1/R1+1/R2+1/R3)? I've only ever seen the equation written like that once before, and I'm wondering if there's a reason as to why it's never really used?
 
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What's easier to use depends on what you have and where you want to go.
The 1/R expression is easier to understand and to remember:

Voltage is the same for all R
Total current = Voltage / Total resistance
Total current = Sum of individual currents = Sum ( Voltage / Individual resistance i )​

Divide by Voltage and you get the 1/R = Sum (1/Ri )
 
CheesyPeeps said:
I'm wondering if there's a reason as to why it's never really used?
It is USED plenty. Students are expected to be able to divide easily.

Similarly, Newton's 2nd law is almost always written F=ma, even though students are expected to recognize and use the equivalent a=F/m and m=F/a.
 
Thanks! I suppose it does make sense that we don't write it that way.
 
What others said. The two equations are mathematically the same. If anything the second form of the equation is used more frequently.
 

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