Jump to content

Help solving a differential equation problem


KFS

Recommended Posts

The problem says: The equation R(dQ/dt)+Q/C=E describes the charge Q on a capacitor, where R, C, and E are constants. (a) Find Q as a function of time if Q=0 at t=0. (b) How long does it take for Q to attain 99% of its limiting charge?

I solved (a) and I got Q=-exp(-t/RC+ln(EC))+EC. But I don't know how to solve (b), I don't know what to equal Q to solve for t. 

Link to comment
Share on other sites

3 hours ago, KFS said:

The problem says: The equation R(dQ/dt)+Q/C=E describes the charge Q on a capacitor, where R, C, and E are constants. (a) Find Q as a function of time if Q=0 at t=0. (b) How long does it take for Q to attain 99% of its limiting charge?

I solved (a) and I got Q=-exp(-t/RC+ln(EC))+EC. But I don't know how to solve (b), I don't know what to equal Q to solve for t. I tried making Q=-exp(-t/RC+ln(EC))+EC=EC but I can't take logarithms to find t.

 

Link to comment
Share on other sites

As t goes to infinity the exponential goes to 0.  Because the exponential is always positive and is subtracted, the "limiting charge" is when that exponential goes to 0 so is EC.  You want to find t such that Q= -exp{-t/RC+ ln(EC)+ EC= -ECexp{-t/RC}+ EC= 0.99EC that is the same as -ECexp{-t/RC}= -0.01EC or exp{-t/RC}= 0.01.

Edited by HallsofIvy
Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.