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Chapter 23

Alternating Current Circuits

23.1 Capacitors and Capacitive Reactance

The resistance in a purely resistive circuit has the same valueat all frequencies.

V rms= I rmsR

23.1 Capacitors and Capacitive Reactance

V rms= I rms X C X C=1

2π fC

capacitive reactance

23.1 Capacitors and Capacitive Reactance

Example 1 A Capacitor in an AC Circuit

The capacitance is 1.50μF and the rms voltage is 25.0 V. What is the rms currentwhen the frequency is (a) 100 Hz and(b) 5000 Hz?

23.1 Capacitors and Capacitive Reactance

I rms=V rms

X C=

25. 0 V1060

=0 .0236 A

X C=1

2π fC=

1

2π 100 Hz 1 .50×10−6F =1060(a)

(b) X C=1

2π fC=

1

2π 5000 Hz 1 .50×10−6F =21. 2

I rms=V rms

X C=

25.0 V21.2

=1. 18 A

23.1 Capacitors and Capacitive Reactance

For a purely resistive circuit,the current and voltage arein phase.

23.1 Capacitors and Capacitive Reactance

The current in a capacitor leadsthe voltage across the capacitorby a phase angle of 90 degrees.

The average power used by a capacitor in an ac circuit is zero.

23.1 Capacitors and Capacitive Reactance

In the phasor model, the voltageand current are represented by rotating arrows (called phasors).

These phasors rotate at a frequency f.

The vertical component of the phasoris the instantaneous value of the currentor voltage.

23.2 Inductors and Inductive Reactance

V rms= I rms X L

inductive reactance

X L=2 fLπ

23.2 Inductors and Inductive Reactance

The current lags behind the voltage by a phase angle of90 degrees.

The average power used by an inductor in an ac circuit is zero.

23.2 Inductors and Inductive Reactance

23.3 Circuits Containing Resistance, Capacitance, and Inductance

In a series RLC circuit, the total opposition to the flow is called the impedance.

V rms= I rmsZ Z= R2 X L−X C 2

23.3 Circuits Containing Resistance, Capacitance, and Inductance

Z= R2 X L−X C 2

23.3 Circuits Containing Resistance, Capacitance, and Inductance

tanφ=V L−V CV R

=X L−X CR

phase angle between current and total voltage

P= I rms2 Z cosφ= I rmsV rms cosφ

23.3 Circuits Containing Resistance, Capacitance, and Inductance

Conceptual Example 4 The Limiting Behavior ofCapacitors and Inductors

The rms voltage of the generator is the same in eachcase. The values of the resistance, capacitance, andinductance are the same. The frequency of the ac generator is very near zero.

In which circuit does the generator supply more rmscurrent?

23.4 Resonance in Electric Circuits

Resonance occurs when the frequency of a vibrating force exactlymatches a natural (resonant) frequency of the object to which the force is applied.

The oscillation of a mass on a spring is analogous to the oscillation of the electric and magnetic fields that occur, respectively, in a capacitorand an inductor.

23.4 Resonance in Electric Circuits

I rms=V rms

R22π fL−1 /2π fC 2

Z= R2 2π fL−1/2π fC 2

Resonant frequency f o=1

2π LC

23.5 Semiconductor Devices

Semiconductor devices such as diodes and transistors are widelyused in modern electronics.

23.5 Semiconductor Devices

n-TYPE AND p-TYPE SEMICONDUCTORS

The semiconducting materials (silicon and germanium) used to make diodes and transistors are doped by adding smallamounts of an impurity element.

23.5 Semiconductor Devices

THE SEMICONDUCTOR DIODE

23.5 Semiconductor Devices

At the junction between the n and p materials, mobile electrons andholes combine and create positive and negative charge layers.

23.5 Semiconductor Devices

There is an appreciable current through the diode when the diode is forward biased.

Under a reverse bias, there is almost no current through the diode.

23.5 Semiconductor Devices

23.5 Semiconductor Devices

A half-wave rectifier.

23.5 Semiconductor Devices

SOLAR CELLS

23.5 Semiconductor Devices

TRANSISTORS

A bipolar junction transistor canbe used to amplify a smaller voltage into a larger one.

23.5 Semiconductor Devices

23.5 Semiconductor Devices