Solving for Time Elapsed in an RC Circuit

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To determine how many time constants have elapsed when a capacitor in an RC circuit reaches 80% of its final charge, the exponential charging formula is essential. This formula involves the time constant τ, which is equal to RC (resistance multiplied by capacitance). By setting the final charge to 100% and the charge at time t to 80%, one can solve for t. The solution will yield a result that is typically between 1*RC and 2*RC. Understanding this relationship is crucial for analyzing the charging behavior of capacitors in RC circuits.
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Homework Statement



For the following questions, consider a charging RC circuit, and let the time constant be represented by τ.
How many time constants have elapsed when the capacitor has 80.0% of its final charge?

Homework Equations


I have no clue! i just need a nudge.


The Attempt at a Solution

 
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You need the formula for how a capacitor charges as a function of time.
I recall it is exponential with a t/(RC) in the exponent. Likely you can find it in the Wikipedia article for "capacitor" if you don't have it handy.
Once you have the formula, set the final charge to 100 and the charge at time t to 80. Then solve for t. It should come out to 1*RC or 2*RC (more likely something in between).
 
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