ECE 3810 First Order Circuit Transients

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ECE 3810 Fundamentals of Electrical Engineering
First Order Transient Response of RL and RC
Circuits

• First Order Transient Characteristics
• A single energy storage element, one C or one L
• Losses represented by one or more R
• Constant sources
• A switch that opens or closes at a given time t
• All linear components

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ECE 3810 Fundamentals of Electrical Engineering I
Transients

• The time-varying currents and voltages resulting
  from the sudden application of sources, usually
  due to switching, are called transients.
• By writing circuit equations, we obtain
  integrodifferential equations.

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ECE 3810 Fundamentals of Electrical Engineering
Series RL Circuit
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ECE 3810 Fundamentals of Electrical Engineering
Series RC Circuit
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ECE 3810 Fundamentals of Electrical Engineering
General First Order Differential Equation
Solution of First Order Differential Equation
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ECE 3810 Fundamentals of Electrical Engineering
Determination of constants in the solution
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ECE 3810 Fundamentals of Electrical Engineering
Determination of constants in the solution
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ECE 3810 Fundamentals of Electrical Engineering
Determination of constants in the solution
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ECE 3810 Fundamentals of Electrical Engineering
General forms of Differential Equation and
Solution
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ECE 3810 Fundamentals of Electrical Engineering
Series RL Circuit
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ECE 3810 Fundamentals of Electrical Engineering
Series RC Circuit
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ECE 3810 Fundamentals of Electrical Engineering
First Order Transient Response of RL and RC
Circuits

• Steps of Solution
• Find the time constant t (RC or L/R)
• Find the initial value of the voltage or current
• Find the final or steady state value of the
  voltage or current
• Substitute the values in the general form of the
  solution