Notes
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Outline
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Alexander-Sadiku
Fundamentals of Electric Circuits
  • Chapter 7
  • First-Order Circuits
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First-Order Circuits
Chapter 7
  • 7.1 The Source-Free RC Circuit
  • 7.2 The Source-Free RL Circuit
  • 7.3 Unit-step Function
  • 7.4  Step Response of an RC Circuit
  • 7.5 Step Response of an RL Circuit
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7.1 The Source-Free
RC Circuit (1)
  • A first-order circuit is characterized by a first-order differential equation.
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7.1 The Source-Free
RC Circuit (2)
  • The natural response of a circuit refers to the behavior (in terms of voltages and currents) of the circuit itself, with no external sources of excitation.
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7.1 The Source-Free
RC Circuit (3)
  •   The key to working with a source-free RC circuit is finding:
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7.1 The Source-Free
RC Circuit (4)
  • Example 1
  •   Refer to the circuit below, determine vC, vx, and io for t ≥ 0.
  •   Assume that vC(0) = 30 V.
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7.1 The Source-Free
RC Circuit (5)
  • Example 2
  •    The switch in circuit below is opened at t = 0, find v(t) for t ≥ 0.
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7.2 The Source-Free
RL Circuit (1)
  • A first-order RL circuit consists of a inductor L (or its equivalent) and a resistor (or its equivalent)
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7.2 The Source-Free
RL Circuit (2)
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7.2 The Source-Free
RL Circuit (3)
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7.2 The Source-Free
RL Circuit (4)
  •   The key to working with a source-free    RL circuit is finding:
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7.2 The Source-Free
RL Circuit (5)
  • Example 3
  •    Find i and vx in the circuit.
  • Assume that i(0) = 5  A.
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7.2 The Source-Free
RL Circuit (6)
  • Example 4
  •    For the circuit, find i(t) for t > 0.
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7.3 Unit-Step Function (1)
  • The unit step function u(t) is 0 for negative values of t and 1 for positive values of t.
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7.3 Unit-Step Function (2)

    • voltage source.





    • for current source:
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7.4 The Step-Response
of a RC Circuit (1)
  • The step response of a circuit is its behavior when the excitation is the step function, which may be a voltage    or a current source.
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7.4 The Step-Response
of a RC Circuit (2)
  • Integrating both sides and considering the initial conditions, the solution of the equation is:
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7.4 The Step-Response
of a RC Circuit (3)
  •   Three steps to find out the step response of an RC circuit:
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7.4 The Step-Response
of a RC Circuit (4)
  • Example 5
  •   Find v(t) for t > 0 in the circuit in below. Assume the switch has been open for a long time and is closed at t = 0.
  •   Calculate v(t) at t = 0.5.
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7.5 The Step-response
of a RL Circuit (1)
  • The step response of a circuit is its behavior when the excitation is the step function, which may be a voltage or a current source.
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7.5 The Step-Response
of a RL Circuit (2)
  •    Three steps to find out the step response of an RL circuit:
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7.5 The Step-Response
of a RL Circuit (4)
  • Example 6
  •    The switch in the circuit shown below has been closed for a long time. It opens at t = 0.
  •     Find i(t) for t > 0.