Conceptual Question about Equivalent Resistance

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SUMMARY

The discussion centers on understanding equivalent resistance in circuit diagrams, specifically for circuits A and B. Circuit B is confirmed to be in parallel, with the equivalent resistance calculated using the formula 1/R = 1/R1 + 1/R2. Circuit A is also established as being equivalent to circuit B, regardless of the physical layout of the resistors, as long as the connections remain intact. The key takeaway is that the arrangement of resistors does not affect their equivalent resistance as long as they connect the same two points.

PREREQUISITES
  • Basic understanding of circuit diagrams
  • Knowledge of electrical resistance and Ohm's Law
  • Familiarity with series and parallel resistor configurations
  • Ability to apply the formula for equivalent resistance in parallel circuits
NEXT STEPS
  • Study the principles of series and parallel circuits in detail
  • Learn how to analyze complex circuit diagrams
  • Explore the concept of equivalent resistance in more advanced circuits
  • Practice calculating equivalent resistance using various resistor configurations
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Students studying electrical engineering, hobbyists learning about circuit design, and educators teaching concepts of resistance and circuit analysis.

jumbogala
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Homework Statement


I don't quite understand how to read circuit diagrams, so I'm not sure how to find the equivalent resistance in some cases.

What is the equivalent resistance of circuits A and B?

I drew a picture to help me explain what I'm talking about:
Circuits.jpg



Homework Equations





The Attempt at a Solution


I know circuit B is definitely in parallel, so the equivalent resistance is 1/R = 1/R1 + 1/R2.

But is circuit A in parallel, too? I think it is but I'm not 100 % sure.
 
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jumbogala said:
What is the equivalent resistance of circuits A and B?

I drew a picture to help me explain what I'm talking about:
Circuits.jpg



Homework Equations



The Attempt at a Solution


I know circuit B is definitely in parallel, so the equivalent resistance is 1/R = 1/R1 + 1/R2.

But is circuit A in parallel, too? I think it is but I'm not 100 % sure.
You are correct -- the two circuits are absolutely equivalent. It does not matter how you draw the resistance R2 as long as it is there somewhere between the two points where the wires from R2 join the wire containing R1.

"Parallel" does not mean that the resistances have to be literally parallel.
 

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