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Chapter 36. AC Circuits

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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.

Topics:

- AC Sources and Phasors
- Capacitor Circuits
- RC Filter Circuits
- Inductor Circuits
- The Series RLC Circuit
- Power in AC Circuits

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

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.

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°.

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.

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°.

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.

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:

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

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

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

Consider the parallel RLC circuit