Parallel Circuits: Resistance Decrease/Current Increase Explained

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Discussion Overview

The discussion centers on the behavior of resistance and current in parallel circuits, specifically addressing why resistance decreases and current increases as more loads are added. The scope includes mathematical explanations, physical principles, and analogies to clarify the concepts involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant requests a detailed explanation of the relationship between resistance and current in parallel circuits, indicating a need for clarity in mathematical and physical terms.
  • Another participant explains that adding loads in parallel creates additional pathways for current, thereby reducing total resistance and increasing current flow, supported by the formula for total resistance in parallel circuits.
  • A further contribution highlights that resistance is inversely proportional to the cross-sectional area of resistors, suggesting that adding resistors in parallel increases the effective cross-sectional area, which affects current distribution.
  • One participant uses an analogy of bypass surgery to illustrate the concept of current paths in parallel circuits.
  • Another participant provides a water analogy comparing different types of filters to explain how parallel connections can increase overall flow rate, relating it back to current and resistance in electrical circuits.

Areas of Agreement / Disagreement

Participants generally agree on the principles of how parallel circuits function, but there are various analogies and explanations presented, indicating a range of perspectives on how to conceptualize the behavior of current and resistance.

Contextual Notes

Some assumptions about ideal conditions (e.g., constant voltage source) are present in the discussion, and the effectiveness of analogies may vary based on individual understanding.

Who May Find This Useful

This discussion may be useful for students or individuals seeking to understand the principles of parallel circuits, particularly those looking for mathematical and conceptual explanations or illustrative analogies.

bob4000
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can anyone please explain to me, in terms of maths, physics and all other elements involved, why the resistance decreases/current increases in a parallel circuit as the amount of loads increase. i just need to have it in words that i can put on paper, i know the rough idea. thanks
 
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Everytime you add an additional load (in parallel), you create a new path for current to travel. Now the circuit is not limited by the value of resistance of the first pathway. It's been bypassed in a way limited by the resistance value of the second pathway. So, the total value of resistance for the entire circuit has been reduced. If you add another pathway, the overall resistance of the circuit will be reduced even further as a result of that new pathway.

RT=1/((1/R1)+(1/R2)+(1/R3)+...)

If you reduce the amount of resistance in the circuit, you increase the amount of amps flowing through the entire circuit.

I = E/RT

Where I= Amps, E= Volts, and RT= Total Ohms

Hope this helps...
 
To add to Metallicbeing's response:

Recall (or realize) that the resistance is inversely proportional to the cross-sectional area [of a cylindrical ohmic resistor]:

[tex]R=\frac{\rho \ell}{A}[/tex]

Adding a second resistor in parallel to the first effectively increases the cross-sectional area of the combination of resistors. Assuming an ideal constant voltage source across the first resistor [and other resistors in parallel with it], the current through the first resistor is unchanged. However, now there is an additional current through the second resistor.
 
It's like bypass surgery.
 
If you want to simplify it, think about this:

You have two kinds of filters:
A - light screen mesh, allows a high flow (10L/s)
B - thicker carbon filter, allows a low flow (1L/s)

You put A into a circuit, its allowing 10L/s to move through it. Now if you connect filter B parallel to A you're allowing an additional 1L/s through. A total of 11L/s.

Water analogies always help with simple electronics.

Difference in potential:
voltage
pressure

Flow rate:
current
current

Resistance:
resistance
restrictive orfice
 
:biggrin: thanks guys, that's helped me a lot :biggrin:
 

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