Find di/dt for RC circuit and show current reaches zero after one time constant

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jendrix
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Homework Statement



Use current equation and find di/dt expression, hence show if initial gradient were maintained the current would be 0 after 1 time constant.



Homework Equations



I calculated RC to be 0.5s i=0.02e^-t/0.5



The Attempt at a Solution



I solved di/dt to be

-0.04e^-2t

i'm stuck where to go next though, can anyone help? Thanks :)
 
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We are not mind readers, please post a COMPLETE problem description and show us your work.
 
Sorry I didn't realize it was linked.The initial circuit was an RC circuit with 100v source in series with a 100uf capacitor and 5kohm resistor.I was then tasked with graphing i vs t for the first 3 seconds and drawing it.After 3 seconds i=5*10^-5

The formula for i was given as 0.02e^-2t

Then calculated CR to be 0.5

Then I had to draw a tangent and estimate the gradient which came out at 0.02/-1.1=-0.018

Then came the question that was asked, hope that helps.
 
You differentiated to find the general equation for gradient as a function of time? Well, when you need to know the gradient at some time t1 you simply substitute the value of t1 for t in your general equation for gradient.

Initial gradient is usually the gradient when t = 0 secs.
 
Thanks, so the gradient would be -0.04, so after 0.5s( one time constant) the current will have dropped by 0.02, so the current will be 0 after one time constant.Thanks so much for your help. :)