Is 1 Second Equal to 1 Ohm Times 1 Farad in RC Circuits?

  • Context: Undergrad 
  • Thread starter Thread starter Zifles
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Discussion Overview

The discussion centers around the relationship between resistance, capacitance, and time in RC circuits, specifically exploring whether 1 second can be expressed as the product of 1 ohm and 1 farad. The scope includes theoretical considerations and dimensional analysis.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions how to demonstrate that the RC circuit has dimensions of time, suggesting that 1 second equals 1 ohm times 1 farad.
  • Another participant proposes expanding Ohm and Farad in terms of base units and simplifying to explore the relationship.
  • A participant mentions the time constant of an RC circuit, stating that it equals R x C, implying that this confirms the dimensionality of time.
  • Some participants express a preference for using established laws, such as Ohm's Law and the relationship between charge, capacitance, and voltage, to aid in the analysis.
  • There is a concern from one participant about relying on a technician's suggestion, feeling it may not be a rigorous approach.
  • Another participant agrees that the time constant indicates that the product of R and C must yield seconds, but emphasizes the need to determine the dimensions of R and C accurately.
  • References are made to a similar discussion involving volts, webers, and seconds, indicating that dimensional analysis is a recurring theme in these contexts.

Areas of Agreement / Disagreement

Participants generally agree on the need to analyze the dimensions of resistance and capacitance, but multiple approaches and interpretations exist regarding how to rigorously demonstrate the relationship to time. The discussion remains unresolved with no consensus on the best method.

Contextual Notes

Limitations include potential missing assumptions in dimensional analysis, dependence on definitions of units, and unresolved steps in the mathematical simplification process.

Zifles
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How can I show that the RC circuit has dimensions of time? 1 second = 1ohm x 1farad?
 
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Expand out Ohm and Farad in terms of base units and simplify.
 
time constant = R x C
 
DaleSpam said:
Expand out Ohm and Farad in terms of base units and simplify.
Ohm's Law and the well-known relation between Q,C & V will help with that.

Or use technician's suggestion, but somehow that feels like a cheat to me.
 
Redbelly98 said:
Ohm's Law and the well-known relation between Q,C & V will help with that.

Or use technician's suggestion, but somehow that feels like a cheat to me.
I agree! The time constant confirms that RC must be seconds but you do need to determine the dimensions of R and C.
You have a similar post regarding volts, webers and seconds. Faradays law gets you started but here also the quantities webers, volts etc need to be expressed as dimensions
 

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