© 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.

© 2012 Pearson Education, Inc. { Chapter 31 Alternating Current Circuits

© 2012 Pearson Education, Inc. Phasors and alternating currents  The left diagram shows the voltage across an AC source as a function of time  On the right is a simple phasor diagram.

© 2012 Pearson Education, Inc. D’Arsonval galvanometer A d’Arsonval galvanometer measures the current through it (see Figures and below). A d’Arsonval galvanometer measures the current through it (see Figures and below). Many analog electrical instruments, such as ammeters and voltmeters, use a galvanometer in their design. Many analog electrical instruments, such as ammeters and voltmeters, use a galvanometer in their design.

© 2012 Pearson Education, Inc. Root-mean-square values  To measure alternating current you need something more complicated than a simple analog voltmeter – e.g., a circuit like the one to the right.

© 2012 Pearson Education, Inc. Resistor in an ac circuit Ohm’s Law gives the voltage amplitude across a resistor: V R = IR. Ohm’s Law gives the voltage amplitude across a resistor: V R = IR. Figure 31.7 shows the circuit, the current and voltage as functions of time, and a phasor. Figure 31.7 shows the circuit, the current and voltage as functions of time, and a phasor.

© 2012 Pearson Education, Inc. Inductor in an ac circuit The voltage amplitude across the inductor The voltage amplitude across the inductor is V L = IX L. is V L = IX L. The voltage leads the current by 90 ◦ The voltage leads the current by 90 ◦

© 2012 Pearson Education, Inc. Capacitance in an ac circuit The voltage amplitude across the capacitor The voltage amplitude across the capacitor is V C = IX C is V C = IX C The voltage follows the current by 90 ◦ The voltage follows the current by 90 ◦

© 2012 Pearson Education, Inc. Comparing ac circuit elements Table 31.1 summarizes the characteristics of a resistor, an inductor, and a capacitor in an ac circuit. Table 31.1 summarizes the characteristics of a resistor, an inductor, and a capacitor in an ac circuit. Figure (below) shows graphs of resistance and reactance. Figure (below) shows graphs of resistance and reactance.

© 2012 Pearson Education, Inc. A useful application: the loudspeaker The woofer (low tones) and the tweeter (high tones) are connected in parallel across the amplifier output. (See Figure shown here.) The woofer (low tones) and the tweeter (high tones) are connected in parallel across the amplifier output. (See Figure shown here.)

© 2012 Pearson Education, Inc. 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 v ab across the resistor? Q31.1 A. i is maximum at the same time as v ab. B. i is maximum one-quarter cycle before v ab. C. i is maximum one-quarter cycle after v ab. D. not enough information given to decide

© 2012 Pearson Education, Inc. 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 v ab across the resistor? A31.1 A. i is maximum at the same time as v ab. B. i is maximum one-quarter cycle before v ab. C. i is maximum one-quarter cycle after v ab. D. not enough information given to decide

© 2012 Pearson Education, Inc. 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 v ab across the inductor? Q31.2 A. i is maximum at the same time as v ab. B. i is maximum one-quarter cycle before v ab. C. i is maximum one-quarter cycle after v ab. D. not enough information given to decide

© 2012 Pearson Education, Inc. 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 v ab across the inductor? A31.2 A. i is maximum at the same time as v ab. B. i is maximum one-quarter cycle before v ab. C. i is maximum one-quarter cycle after v ab. D. not enough information given to decide

© 2012 Pearson Education, Inc. 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 v ab across the capacitor? Q31.3 A. i is maximum at the same time as v ab. B. i is maximum one-quarter cycle before v ab. C. i is maximum one-quarter cycle after v ab. D. not enough information given to decide

© 2012 Pearson Education, Inc. 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 v ab across the capacitor? A31.3 A. i is maximum at the same time as v ab. B. i is maximum one-quarter cycle before v ab. C. i is maximum one-quarter cycle after v ab. D. not enough information given to decide