© 2012 Pearson Education, Inc. A current i flows through an inductor L in the direction from point b toward point a. There is zero resistance in the wires

© 2012 Pearson Education, Inc.

A current i flows through an inductor L in the direction from point b toward point a. There is zero resistance in the wires of the inductor. If the current is decreasing,

A30.2

A. the potential is greater at point a than at point b.

B. the potential is less at point a than at point b.

C. The answer depends on the magnitude of di/dt compared to the magnitude of i.

D. The answer depends on the value of the inductance L.

E. both C. and D. are correct.


{{Chapter 31Chapter 31

Alternating Current CircuitsAlternating Current Circuits


Phasors and alternating currentsPhasors and alternating currents The left diagram shows the voltage across an AC source The left diagram shows the voltage across an AC source

as a function of timeas a function of time On the right is a simple phasor diagram.On the right is a simple phasor diagram.


D’Arsonval galvanometerD’Arsonval galvanometer• A A d’Arsonval galvanometerd’Arsonval galvanometer measures the current measures the current

through it (see Figures 26.13 and 26.14 below).through it (see Figures 26.13 and 26.14 below).• Many analog electrical instruments, such as Many analog electrical instruments, such as

ammeters and voltmeters, use a galvanometer in ammeters and voltmeters, use a galvanometer in their design.their design.


Root-mean-square valuesRoot-mean-square values To measure alternating current you To measure alternating current you

need something more complicated need something more complicated than a simple analog voltmeter – than a simple analog voltmeter – e.g., a circuit like the one to the e.g., a circuit like the one to the right.right.


Resistor in an ac circuitResistor in an ac circuit

• Ohm’s Law gives the Ohm’s Law gives the voltage amplitude across voltage amplitude across a resistor: a resistor: VVRR = IR = IR..

• Figure 31.7 shows the Figure 31.7 shows the circuit, the current and circuit, the current and voltage as functions of voltage as functions of time, and a phasor.time, and a phasor.


Inductor in an ac circuitInductor in an ac circuit

• The voltage amplitude across the inductor The voltage amplitude across the inductor

is is VVLL = IX = IXLL..• The voltage The voltage leadsleads the current by 90 the current by 90◦◦


Capacitance in an ac circuitCapacitance in an ac circuit

• The voltage amplitude across the capacitorThe voltage amplitude across the capacitor is is VVCC = IX = IXCC • The voltage The voltage followsfollows the current by 90 the current by 90◦◦


Comparing ac circuit elementsComparing ac circuit elements

• Table 31.1 summarizes the characteristics of a Table 31.1 summarizes the characteristics of a resistor, an inductor, and a capacitor in an ac resistor, an inductor, and a capacitor in an ac circuit.circuit.

• Figure 31.11 (below) shows graphs of resistance Figure 31.11 (below) shows graphs of resistance and reactance.and reactance.


A useful application: the loudspeakerA useful application: the loudspeaker

• The woofer (low tones) The woofer (low tones) and the tweeter (high and the tweeter (high tones) are connected in tones) are connected in parallel across the parallel across the amplifier output. (See amplifier output. (See Figure 31.12 shown here.)Figure 31.12 shown here.)


A resistor is connected across an ac source as shown. For this circuit, what is the relationship between the instantaneous current i through the resistor and the instantaneous voltage vab across the resistor?

Q31.1

A. i is maximum at the same time as vab.

B. i is maximum one-quarter cycle before vab.

C. i is maximum one-quarter cycle after vab.

D. not enough information given to decide


A resistor is connected across an ac source as shown. For this circuit, what is the relationship between the instantaneous current i through the resistor and the instantaneous voltage vab across the resistor?

A31.1






An inductor is connected across an ac source as shown. For this circuit, what is the relationship between the instantaneous current i through the inductor and the instantaneous voltage vab across the inductor?

Q31.2






An inductor is connected across an ac source as shown. For this circuit, what is the relationship between the instantaneous current i through the inductor and the instantaneous voltage vab across the inductor?

A31.2






A capacitor is connected across an ac source as shown. For this circuit, what is the relationship between the instantaneous current i through the capacitor and the instantaneous voltage vab across the capacitor?

Q31.3






A capacitor is connected across an ac source as shown. For this circuit, what is the relationship between the instantaneous current i through the capacitor and the instantaneous voltage vab across the capacitor?

A31.3





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© 2012 Pearson Education, Inc. A current i flows through an inductor L in the direction from point b toward point a. There is zero resistance in the wires