Time Constant: Why \tau = RC and 63%?

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SUMMARY

The time constant \(\tau\) in electrical circuits is defined as the product of resistance (R) and capacitance (C), expressed as \(\tau = RC\). This relationship indicates that \(\tau\) represents the time it takes for the voltage across a capacitor to rise to approximately 63% of its final value during charging or to decay to 37% during discharging. Understanding this concept is crucial for analyzing transient responses in RC circuits, particularly in filter applications.

PREREQUISITES
  • Basic knowledge of electrical circuits
  • Understanding of resistance (R) and capacitance (C)
  • Familiarity with transient response in RC circuits
  • Ability to interpret circuit diagrams
NEXT STEPS
  • Study the derivation of the time constant formula \(\tau = RC\)
  • Explore the concept of transient analysis in RC circuits
  • Learn about the behavior of filters in response to step inputs
  • Investigate the significance of the 63% threshold in practical applications
USEFUL FOR

Students in electrical engineering, educators teaching circuit theory, and anyone interested in understanding the dynamics of RC circuits and their applications in filtering.

EugP
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I was doing a lab about filters and the professor asked us, as an extra for the lab report, to explain why \tau = RC and why \tau = 63 \% of the total rise or decay.

To be completely honest, I really don't know the answers for either question. I know it makes sense for \tau = RC if you just plug it into the formula.

Anyone have any ideas on how to explain this?
 
Last edited:
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Thank you! that was exactly what I needed!
 

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