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

[EugP]

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?

 

[Doc Al]

Try this: Time Constant for Transients

 

[EugP]

Thank you! that was exactly what I needed!