Lesson 16 Inductors Transient Analysis

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Lesson 16Inductors Transient Analysis
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Learning Objectives

• Calculate inductor voltage and current as a
  function of time.
• Explain inductor DC characteristics.

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Inductor Charging

• Inductor Oppose Changes (Choking effects)
• Inductor is initially fully discharged
• acts like a open circuit
• When switch is closed, the changing current
  across the inductor immediately induces a voltage
  that opposes that change, which keeps the current
  near zero

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Inductor charging

• As current iL builds up, the voltage across the
  R1 resistor increases.

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Inductor Charging Equations

• Voltages and currents in a charging circuit
  change exponentially over time

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Steady State Conditions

• Circuit is at steady state voltage and current
  reach their final values and stop changing
• There is no change in current in the circuit, so
  the inductor has zero voltage induced across it.
  Inductor current will be steady
• Inductor then looks like a short circuit

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The Time Constant

• Rate at which an inductor charges depends on R
  and L, which is called the TIME CONSTANT
• Transients can be considered to last for five
  time constants

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Example Problem 1

• In the circuit below, the switch is initially
  open and conditions are at steady-state.
• After the switch is shut, determine
• how long it will take for the inductor to reach a
  steady-state condition (gt99 of final current).
• Write the equation for the VL(t) iL(t).
  Sketch the transient.
• Find the Energy stored in the Inductor.

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Interrupting Current in an Inductive Circuit

• When switch opens in an RL circuit
• Energy is released in a short time
• This may create a large voltage
• Induced voltage is called an inductive kick
• Opening of inductive circuit may cause voltage
  sparks of thousands of volts

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Interrupting a Circuit

• Switch flashovers are generally undesirable
• They can be controlled with proper engineering
  design
• These large voltages can be useful
• Such as in automotive ignition systems

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Inductor Discharging

• Inductor is initially fully charged with constant
  100 ma current through it. It acts like a short
  circuit
• When switch is opened, the inductor will
  immediately induce a voltage to keep the 100 mA
  current constant.
• KVL can be used to calculate this induced voltage
• Notice the polarity of the induced voltage!

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Inductor Discharging

• As stored energy is released, the induced
  voltage across the inductor drops.
• This makes the voltage drop across the resistor
  drop, so current in the circuit drops

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Inductor Discharging Equations

• Voltages and currents in a discharging circuit
  also change exponentially over time

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The Time Constant

• Rate at which an inductor discharges depends on R
  and L, which is called the TIME CONSTANT
• Transients can be considered to last for five
  time constants

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Example Problem 2

• The circuit shown below has been in operation
  with the switch shut for a long time. The switch
  opens at time t 0, determine
• how long it will take for the inductor to
  discharge.
• Write the equation for the VL, iL,. Sketch the
  transient.