RLC Circuit Analysis

Several linear dynamical systems can be modelled by the 2nd order differential equation with constant coefficients. One of them is a series RLC circuit. In this circuit, a capacitor, inductor and resistor is connected in series with a voltage source, whose voltage E is a function of time.

The equation that models this system is:

Lq" + Rq' + q/C = E(t)

This equation can be solved using the 2nd order ODE solver. For example, if a charged capacitor of capacitance 0.1F is connected to the circuit with L = 1 H and R =10 ohms at time t=0, the equation to be solved becomes:

q" + 10 q' + 10q = 0, initial condition q (t=0) = 1 C

The current in the circuit is q'(t).

It is interesting to see how the plot changes for different values of R.

R=1 ohm

R = 0 ohms