Chapter 1, Problem 15P

As depicted in Fig. P1.15, an RLC circuit consists of three elements: a resistor $\left(\text{R}\right)$, and inductor $\left(\text{L}\right)$ and a capacitor $\left(\text{C}\right)$. The low of current across each element induces a voltage drop.

Kirchhoff's second voltage law states that the algebraic sum of these voltage drops around a closed circuit is zero,

$iR+L\frac{di}{dt}+\frac{q}{C}=0$

where $i=$ current, $R=$ resistance, $L=$ inductance, $t=$ time, $q=$ charge, and $C=$ capacitance. In addition, the current is related to charge as in

$\frac{dq}{dt}=i$

(a) If the initial values are $i\left(0\right)=0\text{ and }q\left(0\right)=1\text{ C}$, use Euler's method to solve this pair of differential equations from $t=0$ to 0.1 s using a step size of $\Delta t=0.01\text{ s}$. Employ the following parameters for your calculation: $R=200\Omega ,L=5\text{ H}$, and $C={10}^{–4}\text{ F}$.

(b) Develop a plot of i and q versus t. Resistor Inductor

FIGURE P1.15