• Learn what is meant by natural response as opposed to step response.
• Learn how to apply Kirchhoff's voltage and current laws to find the differential equation describing an RC or RL first-order circuit which is excited only by initial conditions.
• Know the meaning of the terms first-order, ordinary, constant coefficients, as used to classify a differential equation.
• Learn how to solve the first-order KVL or KCL differential equation to find an expression for the variable. Note that when every term in the equation is a function of either the variable or its derivative, the differential equation is further classified as homogeneous.
• Know what the time-constant is, it's properties, and how to find it for a first-order RL or RC circuit.
• Learn the definitions of transient response and steady-state response for RL and RC circuits excited only by initial conditions.

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

• Be able to write and solve the first-order differential equation for a simple RL or RC circuit.
• Given the solution for one variable of an RL or RC circuit, be able to find the expressions for any other variable in the circuit.
• Be able to use switches and sources to set up initial conditions in RL and RC circuits.
• Be able to find the power and energy dissipated in a first-order circuit as a result of some initial conditions.

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

1. For an RL or RC circuit which is excited only by initial conditions, and given the value of a variable at t₀ and its value at some time t₀, find the value of the time constant for the circuit.

2. For an RL or RC circuit which is excited only by initial conditions, and given the value of a variable at some time t₁ and its value at some other time t₂, where t₁ < t₂, find the value of the time constant for the circuit.

3. In a circuit with a single energy-storage L or C) element and a single resistor, which is excited only by initial conditions, increasing the value of the resistor makes all the variables decay more rapidly. Is the energy-storage element an inductor or a capacitor.

4. How long a value of time (measured as a multiple of the time constant) does it take for a variable to decay to 1 percent of its initial value.