AC Circuits I

1
Chapter 4

• AC Circuits I

2
Objectives

• Write the equation for both an ac sinusoidal
  voltage and sinusoidal current.
• For a sinusoidal function, determine the peak
  value, angular frequency, cyclic frequency,
  period, and phase angle.
• State Eulers equation and discuss its
  significance in establishing ac phasors

3
Objectives

• Discuss the properties of the complex plane and
  show how a phasor is displayed.
• State the rectangular, exponential, and polar
  forms of a phasor and convert among the different
  forms.
• State the ac steady-state voltage-current
  relationships for the three passive parameters.

4
Objectives

• Determine the steady-state ac impedances for the
  three passive parameters.
• Convert a circuit to its ac phasor form with
  sources replaced by phasors and passive
  parameters replaced by their real, imaginary, or
  complex impedances.

5
Objectives

• Solve for phasor voltages and currents in a
  steady-state ac circuit and determine the
  instantaneous forms from the phasors.
• Show how phasors add graphically in a complex
  plane.

6
4-1 Sinusoidal Functions
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Sine Current Function
8
Cosine Current Function
9
General Sinusoidal Current with an Arbitrary
Phase Angle
10
Relative Phase Sequence of Sine and Cosine
Functions
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4-2 Phasors
12
Complex Plane with Phasor Representation
13
Generation of Sinusoidal Function by a Rotating
Phasor
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Examples

• v1(t) 8 sin(1000t 60)
• v2(t) 6 cos(1000t -120)
• i(t) 2 sin(1000t 150)

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Phasor Diagram of Example 4-5
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4-3 AC Voltage-Current Relationships
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Phasor Diagram for Resistance and the
Instantaneous Sinusoidal Forms
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Phasor Diagram for Inductance and the
Instantaneous Sinusoidal Forms
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Phasor Diagram for Capacitance and the
Instantaneous Sinusoidal Forms
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4-4 AC Impedance

• Convert the sinusoidal sources (all at the same
  frequency) to phasors having magnitudes and
  angles.
• Convert all elements in the circuit to their
  steady-state impedance forms as follows
• Resistance values remain the same.
• Inductances are replaced by purely imaginary
  impedances of the form j?L.
• Capacitances are replaced by purely imaginary
  impedances of the form j/?C.
• Various circuit analysis methods may now be
  applied to the circuit to determine voltages or
  currents in phasor forms.
• If it is necessary to determine the instantaneous
  forms, phasors may be converted to those forms.

21
Block Used to Define Impedance
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Resistance and its AC Impedance Form
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Inductance and its AC Impedance Form
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Capacitance and its AC Impedance Form
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RL Circuit of Example 4-6 and its Phasor Form
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RC Circuit of Example 4-7 and its Phasor Form
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RLC Circuit of Example 4-8 and its Phasor Form
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Phasor Diagram for Example 4-8