1. ## Physics-Type Dif EQ

Given that $\displaystyle L = 1$ henry, $\displaystyle R = 100$ ohms, $\displaystyle C = 0.0004$ farad, $\displaystyle E(t) = 30$ volts, $\displaystyle q(0) = 0$ coulombs, $\displaystyle i(0) = 2$ amperes:

1.) Determine the charge on the capacitor and also the current in the above L-R-C circuit.

2.) Determine what the maximum charge is on the capacitor.

2. Not too many physics people here I see. Don't know why they make us learn this junk in a math course when it's not even really math!

3. It's a differential equation so it is entirely a math problem. That doesnt mean that it cant be applicable in physics or a physics problem.

The voltage drop across a linear resistor is IR.
The voltage drop across a capacitor is Q/C.
The voltage drop across an inductor is $\displaystyle L \frac {dI}{dt}$

By Kirchoff's Law:
$\displaystyle L \frac{dI}{dt} + RI + \frac {1}{C}Q = E(t)$

$\displaystyle I = \frac{dQ}{dt}$
$\displaystyle \therefore$
$\displaystyle LQ'' + RQ' + \frac{1}{C}Q = E(t), ~~ Q(t_0) = Q_0, ~~ Q'(t_0) = I(t_0) = I_0$