# Help solving a differential equation problem

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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.

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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.

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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

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