Informal Analysis of DC Circuits

Objectives: We want to be able to
  1. identify various types of dependent source in a circuit diagram. To do so, we will need to be able to identify these features of each dependent source:
    • controlling voltage or current
    • controlled voltage or current
    • gain
    • units of the gain
  2. write and solve the element equation corresponding to a particular dependent source.
  3. identify series and/or parallel elements in a circuit diagram.
  4. label the element currents and voltages of an electric circuit so as to reduce the number of unknowns
  5. identify a dc circuit
  6. analyze dc circuits effectively using the element equations and Kirchhoff's law equations

Reading: Chapter 2 and Sections 3.2.

  • We analyze electric circuits by writing and solving a set of equations.
    • Some of those equation are written using Kirchhoff's laws (Section 3.2).
    • The rest of the equations describe the devices that comprise the circuit. These equations are called "element equations" or "constitutive equations". Chapter 2 presents element equations for the circuit elements that we find in dc circuits: resistors (Section 2.4), independent sources (Section 2.5), open and short circuits (Section 2.5), meters (Section 2.6) and dependent sources (Section 2.7).

Demonstrations: The four types of dependent source: VCVS, VCCS, CCVS, CCCS

Lecture Notes:

  • How can we tell that a circuit is a dc circuit?
    • DC circuits consist of resistors, independent and dependent sources and open and short circuits.
    • The voltages of all independent voltage source are constant and the currents of all independent current sources are constant.
    • Consequently, all of the element voltages and currents in a dc circuit are constant.

  • We analyze dc circuits by writing and solving some algebraic equations. The variables, or unknowns, in these equations are the currents and and voltages of the elements that comprise the dc circuit. These variables represent constant values, i.e. real numbers. It sounds pretty easy. Here are some examples.

  • So far our example circuits have not contained dependents sources. We'll have to work a little harder when there is a dependent source in the circuit. Frequently, the key will be to determine the controlling voltage or current of the dependent source. Here are some examples, some more examples.

  • Sometimes the hardest part of a dc circuit analysis problem is labeling the element currents and voltages. It's useful to have some guidelines for labeling those currents and voltages.
    1. We will will find it useful to recognize series and parallel elements.
    2. Here are guidelines for labeling the elements currents and voltages.

  • We try to write and solve our algebraic equation consecutively but sometimes we must solve simultaneous equations. Here are some examples in which MATLAB is used to solve the simultaneous equations. Additionaly, these examples lead us to make the following observations:
    • Changing the order of series elements will not change the element current or voltage of any circuit element.
    • Changing the order of parallel elements will not change the element current or voltage of any circuit element.


  1. Dependent Sources.
  2. Labeling element currents and voltages: worksheet and solution.
  3. Exercises and solutions.
  4. Wheatstone bridges
  5. Specifications for a dc circuit: worksheet with the solution to the analysis problem and the soltion to the design problem.
  6. How Can We Check...element currents and voltages?

On-line Exercises:

  1. Simple Circuits
  2. Circuits with Dependent Sources

Return to 
ES250 Home Page.