• Learn that the form of the step response for a variable in a second-order RLC circuit consists of a term having the same form as the natural response (which uses the two roots of the characteristic equation ) plus a term having the form of the driving source (a constant).
• Learn that the constants in the solution for the step response can be determined by evaluating the expression and the derivative of the expression for the variable at t = 0 and matching this to the known initial conditions.
• Know how to find the second-order differential equation describing a series RLC circuit by applying Kirchhoff's Voltage Law
• Learn how to find the characteristic equation of the second-order differential equation for a series RLC circuit by assuming an exponential solution.
• Learn the conditions which determine the damping of the second-order circuit, namely, whether the response is overdamped, critically damped, or underdamped. and know the resulting general forms of the response variable.
• Know that once the response is found for the current in the series RLC circuit, the response can be found for any of the branch voltages by simply using the branch equations.

Skills: In studying the material in these sections, you should make certain that you develop the following skills:

• Be able to find the differential equation for a second-order series RLC circuit which is excited only by initial conditions and one which is excited by a constant-valued voltage source and/or initial conditions.
• Be able to find the characteristic equation for a second-order series RLC circuit from its differential equation.
• Be able to determine whether the response will be overdamped, critically damped, or underdamped, and know what the general form of the expression for the response will be for these three cases.

Review Questions: Test your understanding of the material in these sections by answering the following review questions:

1. In the step response for the parallel RLC circuit, what are the values of the final currents in the resistor, the capacitor, and the inductor.

2. In the series RLC circuit, if the element values are such that the response is critically damped, what happens to the damping if the value of the resistor is increased?

3. In the series RLC circuit, if the element values are such that the response is critically damped, what happens to the damping if the value of the inductor is increased?

4. In the series RLC circuit, if the element values are such that the response is critically damped, what happens to the damping if the value of the capacitor is increased?

5. In the step response for the series RLC circuit, what are the values of the final voltages across the resistor, the capacitor, and the inductor.