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

AI Thread Summary
The time constant \(\tau\) is defined as the product of resistance (R) and capacitance (C) in an RC circuit, indicating how quickly a capacitor charges or discharges. The value of \(\tau\) represents the time it takes for the voltage to reach approximately 63% of its final value during charging or to decay to 37% during discharging. This percentage is derived from the mathematical properties of exponential functions, which govern the behavior of RC circuits. Understanding \(\tau\) is essential for analyzing transient responses in electronic circuits. The discussion highlights the importance of grasping these concepts for lab reports and practical applications.
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?
 
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Thank you! that was exactly what I needed!
 

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