1.15 As depicted in Fig. P1.15, an RLC circuit consists of three elements: a resistor (R), and inductor (L) and a capacitor (C). The ow of current across each element induces a voltage drop.

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

iR 1 L di 1 q 5 0 dt C

where i 5 current, R 5 resistance, L 5 inductance, t 5 time, q 5 charge, and C 5 capacitance. In addition, the current is related to charge as in

dq dt 5 i

(a) If the initial values are i(0) 5 0 and q(0) 5 1 C, use Eulers method to solve this pair of differential equations from t 5 0 to 0.1 s using a step size of Dt 5 0.01 s. Employ the following parameters for your calculation: R 5 200 V, L 5 5 H, and C 5 104 F.

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

Send me the plot V=V(t) and your code implementing Euler algorithm.

Explain what will happen with the droplet at t>10 min.

Obtain analytical solution and compare it with the numerical one.