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Chapter 21

Chapter 21. Alternating Current (AC) Circuits and Electromagnetic Waves. Example 21.4 – page 701. A series RLC AC circuit has resistance R=250 Ω , inductance L=0.6H, capacitance C=3.5µF, frequency f=60Hz, and a maximum voltage Vmax=150V. Find A) the impedance

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Chapter 21

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  1. Chapter 21 Alternating Current (AC) Circuits and Electromagnetic Waves

  2. Example 21.4 – page 701 • A series RLC AC circuit has resistance R=250Ω, inductance L=0.6H, capacitance C=3.5µF, frequency f=60Hz, and a maximum voltage Vmax=150V. Find • A) the impedance • B) the maximum current in the circuit • C) the phase angle • D) the maximum voltages across the elements.

  3. Example 21.4 – cont. a) Find the impedance of the circuit.

  4. Example 21.4 – cont. B) Find the maximum current. C) Find the phase angle.

  5. Example 21.4 – cont. D) Find the maximum voltage across the elements.

  6. Power in an AC Circuit • No power losses are associated with pure capacitors and pure inductors in an AC circuit • In a capacitor, during one-half of a cycle energy is stored and during the other half the energy is returned to the circuit • In an inductor, the source does work against the back emf of the inductor and energy is stored in the inductor, but when the current begins to decrease in the circuit, the energy is returned to the circuit

  7. Power in an AC Circuit, cont • The average power delivered by the generator is converted to internal energy in the resistor • Pav = IrmsΔVR = IrmsΔVrms cos  • cos  is called the power factor of the circuit • Phase shifts can be used to maximize power outputs

  8. Example 21.5 – page 703 • Calculate the average power delivered to the series RLC circuit described in example 21.4.

  9. Resonance in an AC Circuit • Resonance occurs at the frequency, ƒo, where the current has its maximum value • To achieve maximum current, the impedance must have a minimum value • This occurs when XL = XC • Then,

  10. Resonance, cont • Theoretically, if R = 0 the current would be infinite at resonance • Real circuits always have some resistance • Tuning a radio • A varying capacitor changes the resonance frequency of the tuning circuit in your radio to match the station to be received • Metal Detector • The portal is an inductor, and the frequency is set to a condition with no metal present • When metal is present, it changes the effective inductance, which changes the current • The change in current is detected and an alarm sounds

  11. Example 21.6 – page 705 • Consider a series RLC circuit for which R=150Ω, L=20mH, Vrms=20V, and f=796s-1. • A) determine the value of the capacitance for which the rms current is maximum. • B) find the maximum rms current in the circuit.

  12. Example 21.6 – cont. • A) determine the value of the capacitance for which the rms current is maximum.

  13. B) find the maximum rms current in the circuit. Example 21.6 – cont.

  14. Transformers • An AC transformer consists of two coils of wire wound around a core of soft iron • The side connected to the input AC voltage source is called the primaryand has N1 turns

  15. Transformers, 2 • The other side, called the secondary, is connected to a resistor and has N2turns • The core is used to increase the magnetic flux and to provide a medium for the flux to pass from one coil to the other • The rate of change of the flux is the same for both coils

  16. Transformers, 3 • The voltages are related by • When N2 > N1, the transformer is referred to as a step uptransformer • When N2 < N1, the transformer is referred to as a step down transformer

  17. Transformer, final • The power input into the primary equals the power output at the secondary • I1ΔV1 = I2ΔV2 • You don’t get something for nothing • This assumes an ideal transformer • In real transformers, power efficiencies typically range from 90% to 99%

  18. Electrical Power Transmission • When transmitting electric power over long distances, it is most economical to use high voltage and low current • Minimizes I2R power losses • In practice, voltage is stepped up to about 230,000 V at the generating station and stepped down to 20,000 V at the distribution station and finally to 120 V at the customer’s utility pole

  19. Example 21.7 – page 706 • A generator at a utility company produces 100A of current at 4000V. The voltage is stepped up to 2.4x105V by a transformer before being sent on a high-voltage transmission line across a rural area to a city. Assume that the effective resistance of the power line is 30Ω and that the transformers are ideal. • A) determine the percentage of power lost in the transmission line. • B) what percentage of the original power would be lost in the transmission line if the voltage were not stepped up?

  20. Example 21.7 – cont. A) determine the percentage of power lost in the transmission line.

  21. B) what percentage of the original power would be lost in the transmission line if the voltage were not stepped up? Example 21.7 – cont.

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