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Unit 7: Parallel AC Circuits

In Unit 6 we saw that analyzing series AC circuits involves the same steps as analyzing series DC circuits, but that at each step you must use complex numbers instead of real numbers. We’ll see in this unit that, as you may have guessed, parallel AC circuits are a lot like parallel DC circuits, except that again you need to use complex numbers throughout the analysis.

Also, the same rules that are useful in analyzing parallel DC circuits (such as Kirchhoff’s Current Law and the Current-Divider Rule) are also useful for parallel AC circuits. Again, though, the math is more complicated because you have to use complex numbers.

We’ll also look at quantities called admittance and susceptance, which are similar to the quantity called conductance that you may recall from your studies of parallel DC circuits. When dealing with parallel circuits, some people find it more convenient to use conductance, susceptance, and admittance in place of resistance, reactance, and impedance. I’m not one of those people, but I do think that you should at least understand what these terms mean and understand how they relate to each other.

Unit 6 Review

Review of Parallel DC Circuits
Review: Kirchhoff’s Current Law in Parallel DC Circuits
Review: Current Divider Rule in Parallel DC Circuits
Review: Troubleshooting Parallel DC Circuits

Analyzing Parallel AC Circuits
Parallel RLC circuit
  • Follow these steps to analyze any parallel AC circuit, such as the parallel RLC circuit shown above:
    1. Recognize that, since we’re dealing with a parallel circuit, each component’s voltage is equal to the source voltage.
    2. Apply Ohm’s law separately to each component to find each component’s current.
    3. Use the reciprocal formula to find the circuit’s total impedance, ZT.
    4. Find the circuit’s total current either by adding all of the components’ currents, or by applying Ohm’s law to the entire circuit.
  • These are very similar to the steps that you followed in EET 1150 to analyze a simple parallel DC circuit containing resistors. The big difference is that throughout this procedure, we must now use complex numbers instead of real numbers.
  • Let’s look at each step in more detail.
  • Step 1: Find Individual Voltage Drops
    Step 2: Find Individual Currents
    Step 3: Find Total Impedance
    Step 4: Find Total Current

    Kirchhoff’s Current Law

    Current-Divider Rule

    Troubleshooting Parallel AC Circuits

    Summary of New Terms
    Admittance of a Resistor
    Admittance of a Capacitor
    Admittance of an Inductor

    Practice Problems

    Unit 7 Review

    Congratulations! You’ve completed the e-Lesson for this unit.