Slide 1Fig 33-CO, p.1033

Slide 2Fig 33-1, p the basic principle of the ac generator is a direct consequence of Faraday’s law of induction. When a conducting loop is rotated in a magnetic field at constant angular frequency ω, a sinusoidal voltage (emf) is induced in the loop. This instantaneous voltage Δv is where ΔV max is the maximum output voltage of the ac generator, or the voltage amplitude, the angular frequency is The voltage supplied by an AC source is sinusoidal with a period T. where f is the frequency of the generator (the voltage source) and T is the period. Commercial electric power plants in the United States use a frequency of 60 Hz, which corresponds to an angular frequency of 377 rad/s.

Slide 3  To simplify our analysis of circuits containing two or more elements, we use graphical constructions called phasor diagrams.  In these constructions, alternating (sinusoidal) quantities, such as current and voltage, are represented by rotating vectors called phasors.  The length of the phasor represents the amplitude (maximum value) of the quantity, and the projection of the phasor onto the vertical axis represents the instantaneous value of the quantity.  As we shall see, a phasor diagram greatly simplifies matters when we must combine several sinusoidally varying currents or voltages that have different phases.

Slide 4Fig 33-2, p.1035 At any instant, the algebraic sum of the voltages around a closed loop in a circuit must be zero (Kirchhoff’s loop rule). where Δv R is the instantaneous voltage across the resistor. Therefore, the instantaneous current in the resistor is the maximum current:

Slide 5Fig 33-3, p.1035

Slide 6Fig 33-3a, p.1035  Plots of the instantaneous current i R and instantaneous voltage  v R across a resistor as functions of time.  The current is in phase with the voltage, which means that the current is zero when the voltage is zero, maximum when the voltage is maximum, and minimum when the voltage is minimum.  At time t = T, one cycle of the time- varying voltage and current has been completed.

Slide 7Fig 33-3b, p.1035 Phasor diagram for the resistive circuit showing that the current is in phase with the voltage. What is of importance in an ac circuit is an average value of current, referred to as the rms current

Slide 8Fig 33-5, p.1037 (a) Graph of the current in a resistor as a function of time (b) Graph of the current squared in a resistor as a function of time. Notice that the gray shaded regions under the curve and above the dashed line for I 2 max /2 have the same area as the gray shaded regions above the curve and below the dashed line for I 2 max /2. Thus, the average value of i 2 is I 2 max /2.

Slide 9 The voltage output of a generator is given by Δv = (200 V)sin ωt. Find the rms current in the circuit when this generator is connected to a 100 Ω- resistor.

Slide 10Fig 33-6, p.1038 is the self-induced instantaneous voltage across the inductor.

Slide 11 the inductive reactance

Slide 12Fig 33-7a, p.1039

Slide 13Fig 33-7b, p.1039

Slide 14 In a purely inductive ac circuit, L = 25.0 mH and the rms voltage is 150 V. Calculate the inductive reactance and rms current in the circuit if the frequency is 60.0 Hz.

Slide 15

Slide 16

Slide 17Fig 33-9, p.1041

Slide 18Fig 33-10, p.1041

Slide 19Fig 33-10a, p.1041

Slide 20Fig 33-10b, p.1041

Slide 21 capacitive reactance:

Slide 22

Slide 23Fig 33-13a, p.1044 Φ the phase angle between the current and the applied voltage  the current at all points in a series ac circuit has the same amplitude and phase

Slide 24

Slide 25Fig 33-13b, p.1044

Slide 26Fig 33-14, p.1044

Slide 27Fig 33-14a, p.1044

Slide 28Fig 33-14b, p.1044

Slide 29Fig 33-14c, p.1044

Slide 30Fig 33-15, p.1045 (a) Phasor diagram for the series RLC circuit The phasor  VR is in phase with the current phasor Imax, the phasor  VL leads Imax by 90°, and the phasor  VC lags Imax by 90°. The total voltage  Vmax makes an Angle  with Imax. (b) Simplified version of the phasor diagram shown in part (a)

Slide 31Fig 33-16, p.1045 An impedance triangle for a series RLC circuit gives the relationship Z  R 2 + (XL - XC) 2

Slide 32Table 33-1, p.1046

Slide 33

Slide 34 the phase angle

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41 No power losses are associated with pure capacitors and pure inductors in an ac circuit When the current begins to increase in one direction in an ac circuit, charge begins to accumulate on the capacitor, and a voltage drop appears across it. When this voltage drop reaches its maximum value, the energy stored in the capacitor is However, this energy storage is only momentary. The capacitor is charged and discharged twice during each cycle: Charge is delivered to the capacitor during two quarters of the cycle and is returned to the voltage source during the remaining two quarters. Therefore, the average power supplied by the source is zero. In other words, no power losses occur in a capacitor in an ac circuit.

Slide 42 For the RLC circuit, we can express the instantaneous power P The average power the quantity cos φ is called the power factor the maximum voltage drop across the resistor is given by

Slide 43 In words, the average power delivered by the generator is converted to internal energy in the resistor, just as in the case of a dc circuit. No power loss occurs in an ideal inductor or capacitor. When the load is purely resistive, then φ= 0, cos φ= 1, and

Slide 44

Slide 45 A series RLC circuit is said to be in resonance when the current has its maximum value. In general, the rms current can be written Because the impedance depends on the frequency of the source, the current in the RLC circuit also depends on the frequency. The frequency ω 0 at which X L -X C =0 is called the resonance frequency of the circuit. To find ω 0, we use the condition XL = XC,from which we obtain, ω 0 L =1/ ω 0 C or

Slide 46Fig 33-19, p.1050 (a) The rms current versus frequency for a series RLC circuit, for three values of R. The current reaches its maximum value at the resonance frequency. (b) Average power delivered to the circuit versus frequency for the series RLC circuit, for two values of R.

Slide 47Fig 33-19a, p.1050

Slide 48Fig 33-19b, p.1050

Slide 49Fig 33-20, p.1051

Slide 50Fig 33-21, p.1052

Slide 51Fig 33-22, p.1052

Slide 52p.1053

Slide 53Fig 33-23, p.1053

Slide 54p.1053

Slide 55Fig 33-24, p.1055

Slide 56Fig 33-24a, p.1055

Slide 57Fig 33-24b, p.1055

Slide 58Fig 33-25, p.1055

Slide 59Fig 33-25a, p.1055

Slide 60Fig 33-25b, p.1055

Slide 61Fig 33-26, p.1056

Slide 62Fig 33-26a, p.1056

Slide 63Fig 33-26b, p.1056

Slide 64Fig Q33-2, p.1058

Slide 65Fig Q33-22, p.1058

Slide 66Fig P33-3, p.1059

Slide 67Fig P33-6, p.1059

Slide 68Fig P33-7, p.1059

Slide 69Fig P33-25, p.1060

Slide 70Fig P33-26, p.1060

Slide 71Fig P33-30, p.1061

Slide 72Fig P33-36, p.1061

Slide 73Fig P33-47, p.1062

Slide 74Fig P33-55, p.1062

Slide 75Fig P33-56, p.1062

Slide 76Fig P33-58, p.1063

Slide 77Fig P33-61, p.1063

Slide 78Fig P33-62, p.1063

Slide 79Fig P33-64, p.1063

Slide 80Fig P33-69, p.1064

Slide 81Fig P33-69a, p.1035

Slide 82Fig P33-69b, p.1035

Slide 83