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Mastering Parallel AC Circuits: Impedance, Laws, and Graphical Analysis

Learn to calculate total impedance, apply Kirchhoff’s Current Law, and visualize voltages and currents in AC parallel circuits. Solve example problems and explore current divider rules.Graphical representations included.

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Mastering Parallel AC Circuits: Impedance, Laws, and Graphical Analysis

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  1. Lesson 17: Parallel AC Circuits

  2. Learning Objectives • Compute the total impedance for AC parallel circuits. • Apply Kirchhoff’s Current Law and the current divider rule to AC parallel circuits. • Graph impedance, voltages and current as function of phase. • Graph voltages and current as a function of time.

  3. Parallel AC Circuit

  4. Example Problem 1 Determine ZT for the following circuit:

  5. What if Z1and Z2 are equal inductive and capacitive reactances? The resulting total impedance is infinite, so the equivalent is an open circuit. Impedances in Parallel (special case)

  6. The summation of current phasors entering and leaving a node is equal to zero. Kirchhoff’s Current Law (KCL) IF:

  7. Current Divider Rule

  8. Current Divider Rule

  9. Example Problem 2 Find ZT, IT, I1, I2, I3 However, ZC and ZL are not given in reactances, they are given as capacitance and inductance respectively. We need to convert to reactance:

  10. Example Problem 3 • Find the total impedance ZT. • Determine the supply current (IT,) using the current divider rule • Calculate IC and IR. • Verify KCL. Same as +210⁰

  11. Example Problem 3 Graphically

  12. QUESTIONS?

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