RC Circuit Analysis: Find di/dt & Show Current=0 After 1 Time Constant

[jendrix]

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 :)

 

[Integral]

We are not mind readers, please post a COMPLETE problem description and show us your work.

 

[jendrix]

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.

 

[NascentOxygen]

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.

 

[jendrix]

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. :)