Chapter 36. AC Circuits

1. Chapter 36. AC Circuits Today, a “grid” of AC electrical distribution systems spans the United States and other countries. Any device that plugs into an electric outlet uses an AC circuit. In this chapter, you will learn some of the basic techniques for analyzing AC circuits. Chapter Goal: To understand and apply basic techniques of AC circuit analysis.

2. Chapter 36. AC Circuits Topics: • AC Sources and Phasors • Capacitor Circuits • RC Filter Circuits • Inductor Circuits • The Series RLC Circuit • Power in AC Circuits

3. AC Sources and Phasors

4. AC Sources and Phasors

5. AC Circuits In an AC resistor circuit, Ohm’s law applies to both the instantaneous and peak currents and voltages.

6. AC Circuits The resistor voltagevR is given by where VR is the peak or maximum voltage. The current through the resistor is where IR = VR/R is the peak current.

8. Capacitor Circuits The instantaneous voltage across a single capacitor in a basic capacitor circuit is equal to the instantaneous emf: Where VC is the maximum voltage across the capacitor, also equal to the maximum emf. The instantaneous current in the circuit is The AC current to and from a capacitor leads the capacitor voltage by π/2 rad, or 90°.

9. Capacitive Reactance The capacitive reactance XC is defined as The units of reactance, like those of resistance, are ohms. Reactance relates the peak voltage VC and current IC: NOTE: Reactance differs from resistance in that it does not relate the instantaneous capacitor voltage and current because they are out of phase. That is, vC ≠ iCXC.

11. Inductor Circuits The instantaneous voltage across a single inductor in a basic inductive circuit is equal to the instantaneous emf: Where VL is the maximum voltage across the inductor, also equal to the maximum emf. The instantaneous inductor current is The AC current through an inductor lags the inductor voltage by π/2 rad, or 90°.

12. Inductive Reactance The inductive reactance XL is defined as Reactance relates the peak voltage VL and current IL: NOTE: Reactance differs from resistance in that it does not relate the instantaneous inductor voltage and current because they are out of phase. That is, vL ≠ iLXL.

14. The Series RLC Circuit The impedanceZ of a series RLC circuit is defined as Impedance, like resistance and reactance, is measured in ohms. The circuit’s peak current is related to the source emf and the circuit impedance by Z is at a minimum, making I a maximum, when XL = XC, at the circuit’s resonance frequency:

16. Power in AC Circuits The root-mean-square currentIrms is related to the peak current IR by Similarly, the root-mean-square voltage and emf are The average power supplied by the emf is

17. Summary: Important Concepts

18. Important Concepts

19. Applications

20. Applications

21. A series RLC circuit has VC = 5.0 V, VR = 7.0 V, and VL = 9.0 V. Is the frequency above, below or equal to the resonance frequency? • Above the resonance frequency • Below the resonance frequency • Equal to the resonance frequency

22. A series RLC circuit has VC = 5.0 V, VR = 7.0 V, and VL = 9.0 V. Is the frequency above, below or equal to the resonance frequency? • Above the resonance frequency • Below the resonance frequency • Equal to the resonance frequency

23. Consider the parallel RLC circuit