Series RL Circuits

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Series RL Circuits
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Objectives

• Compare and contrast series RL circuits with
  series RC circuits
• Analyze and determine voltages, current,
  impedance, and phase angle in any series RL
  circuits given the necessary parameters.
• Define true power, reactive power, and apparent
  power as they pertain to reactive circuits.
• Determine the three powers mentioned above given
  circuit parameters.
• Determine the power factor of a given reactive
  circuit.
• Discuss inductor quality and its impact on series
  RL circuits.
• Determine the quality factor of an inductor.
• Determine the quality factor of a circuit
  containing an inductor.

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Series RC Circuit
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Series RL Circuit
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Series RC vs RL Comparison

• RC
• ? will be between 0 and -90

• RL
• ? will be between 0 and 90

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Series RC vs RL Comparison

• RC

• RL

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Series RL Analysis

• Determine impedance and phase angle.
• R 56 ?
• XL 100 ?
• Z
• ?

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Series RL Analysis

• Determine circuit Z, ?, and VS
• R 10 K?
• L 100 mH
• f 10 KHz
• Z
• ?
• VS

IT 200 µA
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Series RL Analysis

• Determine source voltage and phase angle.
• VR 50 volts
• VL 35 volts
• VS
• ?

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Power Consumption
Resistive Power (PR) or True Power (PT)
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Power Consumption
Reactive Power (PX) or imaginary power
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Apparent Power (PA) is the vector sum of true
power and reactive power
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Power Factor (PF)

• Ratio of true power to apparent power.
• Measure of the power loss in a circuit.

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Power Factor (PF)

• True power is a function of the pure resistance
  (R) of the circuit.
• Apparent power is a function of the total
  impedance (Z) of the circuit.
• Therefore, the power factor is also a ratio of
  the circuit resistance to the circuit impedance.

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Power Factor (PF)

• Compare the impedance triangle to the power
  triangle.
• R and PR are both the side adjacent to angle ?.
• Z and PA are both the hypotenuse of the triangle.
• The phase angle of a series reactive circuit can
  be found by the cosine of the angle formed by the
  adjacent side and hypotenuse. Therefore

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Inductor Quality Factor (Q)

• An inductor has resistance due to the fact that
  it is simply a piece of wire. All wire has
  resistance.
• This resistance (RW) results in some true power
  being consumed by the inductor.
• Even in a purely inductive circuit, RW is
  present and subtracts for the total energy that
  can be stored in the field.

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Inductor Quality Factor (Q)

• This resistance appears to be in series with the
  inductor.
• Generally speaking, it is very small and can be
  ignored, but in some applications it must be
  considered.

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Quality Factor (Q)

• The quality factor (Q) of a coil is a ratio of
  the energy stored in the field (due to XL) to the
  energy dissipated in the coil by the resistance
  (due to RW).
• Q is a figure of merit and has no unit of
  measurement.

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• A given series RC circuit has the following
• R 2.2 K?
• XC 3.3 K ?
• VS 5 V

• Find
• Z
• I
• ?
• PR
• PX
• PA
• PF

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• A given series RL circuit has the following
• R 39.5 K?
• RW 500 ?
• L 450 mH
• VS 6 V
• f 20 KHz

• Find
• XL
• Z
• I
• ?
• PR
• PX
• PA
• PF
• Inductor Q
• Circuit Q