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Topic | Discussion | Learning Aids
| 23.1 CAPACITORS AND CAPACITIVE REACTANCE In an ac circuit the rms voltage Vrms across a capacitor is related to the rms current Irms by |
Relation between voltage and current |

| (23.1)

where XC is the capacitive reactance. The capacitive reactance is measured in ohms () and is given by
Capacitive reactance |

| (23.2)

where f is the frequency and C is the capacitance.
Phase angle between current and voltage | The ac current in a capacitor leads the voltage across the capacitor by a phase angle of 90° or radians. As a result, a capacitor consumes no power, on average. |
Voltage and current phasors | The phasor model is useful for analyzing the voltage and current in an ac circuit. In this model, the voltage and current are represented by rotating arrows, called phasors. The length of the voltage phasor represents the maximum voltage V0, and the length of the current phasor represents the maximum current I0. The phasors rotate in a counterclockwise direction at a frequency f. Since the current leads the voltage by 90° in a capacitor, the current phasor is ahead of the voltage phasor by 90° in the direction of rotation.
The instantaneous values of the voltage and current are equal to the vertical components of the corresponding phasors.
| 23.2 INDUCTORS AND INDUCTIVE REACTANCE In an ac circuit the rms voltage Vrms across an inductor is related to the rms current Irms by |
Relation between voltage and current |

| (23.3)

where XL is the inductive reactance. The inductive reactance is measured in ohms () and is given by
Inductive reactance |

| (23.4)

where f is the frequency and L is the inductance.
Phase angle between current and voltage | The ac current in an inductor lags behind the voltage across the inductor by a phase angle of 90° or radians. Consequently, an inductor, like a capacitor, consumes no power, on average. |
Voltage and current phasors | The voltage and current phasors in a circuit containing only an inductor also rotate in a counterclockwise direction at a frequency f. However, since the current lags the voltage by 90° in an inductor, the current phasor is behind the voltage phasor by 90° in the direction of rotation.
The instantaneous values of the voltage and current are equal to the vertical components of the corresponding phasors.

Use Self-Assessment Test 23.1 to evaluate your understanding of Sections 23.1 and 23.2.

| 23.3 CIRCUITS CONTAINING RESISTANCE, CAPACITANCE, AND INDUCTANCE When a resistor, a capacitor, and an inductor are connected in series, the rms voltage across the combination is related to the rms current according to |
Relation between voltage and current |

| (23.6)

where Z is the impedance of the combination. The impedance is measured in ohms () and is given by
Impedance |

| (23.7)

where R is the resistance, and XL and XC are, respectively, the inductive and capacitive reactances.
| The tangent of the phase angle between current and voltage in a series RCL circuit is |
Phase angle between current and voltage |

| (23.8)

Only the resistor in the RCL combination consumes power, on average. The average power consumed in the circuit is
Average power consumed Power factor |

| (23.9)

where is called the power factor of the circuit.
| 23.4 RESONANCE IN ELECTRIC CIRCUITS A series RCL circuit has a resonant frequency f0 that is given by |
Resonant frequency |

| (23.10)

where L is the inductance and C is the capacitance. At resonance, the impedance of the circuit has a minimum value equal to the resistance R, and the rms current has a maximum value.

Use Self-Assessment Test 23.2 to evaluate your understanding of Sections 23.3 and 23.4.

n-type semiconductor | 23.5 SEMICONDUCTOR DEVICES In an n-type semiconductor, mobile negative electrons carry the current. An n-type material is produced by doping a semiconductor such as silicon with a small amount of impurity atoms such as phosphorus. |
p-type semiconductor | In a p-type semiconductor, mobile positive “holes” in the crystal structure carry the current. A p-type material is produced by doping a semiconductor with a small amount of impurity atoms such as boron. These two types of semiconductors are used in p-n junction diodes, light-emitting diodes, and solar cells, and in pnp and npn bipolar junction transistors. |

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