(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider an LRC circuit. L = 3/5, R = 10, C = 1/30, E(t) = 300, Q(0)=0, I(0)=0

i) Find charge and current.

ii) Find maximum charge on the capacitor.

2. Relevant equations

LQ'' + RQ' +(1/C)Q = E

3. The attempt at a solution

(3/5)Q'' + 10Q' +30Q = 300

For the roots of characteristic equation I got:

[itex]m = -\frac{25}{3} \pm \frac{5\sqrt{7}}{3}[/itex]

This leads to the solution to the homogenous part, and the particular solution is simply Q=10.

So, after applying initial conditions to find the constants, the full general solution came out to

[itex] Q(t) = (5- \frac{25}{\sqrt{7}})e^{(-\frac{25}{3} + \frac{5\sqrt{7}}{3})t} + (\frac{25}{\sqrt{7}}-15)e^{(-\frac{25}{3}-\frac{5\sqrt{7}}{3})t} +10[/itex]

Differentiating to find the current gives me:

[itex] I(t) = (-\frac{25}{3} + \frac{5\sqrt{7}}{3})(5- \frac{25}{\sqrt{7}})e^{(-\frac{25}{3} + \frac{5\sqrt{7}}{3})t} + (-\frac{25}{3}-\frac{5\sqrt{7}}{3})(\frac{25}{\sqrt{7}}-15)e^{(-\frac{25}{3}-\frac{5\sqrt{7}}{3})t}[/itex]

So that's part i) finished.

But I'm confused on part ii)....

It's asking for the maximum charge on the capacitor, and I assume charge is given by Q(t).

So to find the maximum charge, do I set I=0 and solve for t? Since it says I(0)=0, then wouldn't t=0, which means Q=0?

I'm pretty sure there is more to it then that, but I'm confused.

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# Homework Help: Non-homogenous Diff EQ, LRC circuit

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