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Outline
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Alexander-Sadiku
Fundamentals of Electric Circuits
  • Chapter 6
  • Capacitors and Inductors
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Capacitors and Inductors Chapter 6
  • 6.1 Capacitors
  • 6.2 Series and Parallel Capacitors
  • 6.3 Inductors
  • 6.4 Series and Parallel Inductors
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6.1 Capacitors (1)
  • A capacitor is a passive element designed        to store energy in its electric field.
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6.1 Capacitors (2)
  • Capacitance C is the ratio of the charge q on one plate of a capacitor to the voltage difference v between the two plates, measured in farads (F).
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6.1 Capacitors (3)
  • If i is flowing into the +ve terminal of C
    • Charging => i is +ve
    • Discharging => i is –ve
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6.1 Capacitors (4)
  • The energy, w, stored in the capacitor is
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6.1 Capacitors (5)
  • Example 1


    • The current through a 100-mF capacitor is


    • i(t) = 50 sin(120 pt) mA.


    • Calculate the voltage across it at t =1 ms and
    • t = 5 ms.


    • Take v(0) =0.
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6.1 Capacitors (6)
  • Example 2


    • An initially uncharged 1-mF capacitor has the current shown below across it.


    • Calculate the voltage across it at t = 2 ms and
    • t = 5 ms.
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6.2 Series and Parallel
Capacitors (1)
  • The equivalent capacitance of N parallel-connected capacitors is the sum of the individual capacitances.
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6.2 Series and Parallel
 Capacitors (2)
  • The equivalent capacitance of N series-connected capacitors is the reciprocal of the sum of the reciprocals of the individual capacitances.
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6.2 Series and Parallel
Capacitors (3)
  • Example 3
  •  Find the equivalent capacitance seen at the terminals of the circuit in the circuit shown below:
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6.2 Series and Parallel
Capacitors (4)
  • Example 4
  • Find the voltage across each of the capacitors in the circuit shown below:
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6.3 Inductors (1)
  • An inductor is a passive element designed         to store energy in its magnetic field.
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6.3 Inductors (2)
  • Inductance is the property whereby an inductor exhibits opposition to the change of current flowing through it, measured in henrys (H).
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6.3 Inductors (3)
  • The current-voltage relationship of an inductor:
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6.3 Inductors (4)
  • Example 5
  • The terminal voltage of a 2-H    inductor is
    • v = 10(1-t) V


  •  Find the current flowing through it at    t = 4 s and the energy stored in it within 0 < t < 4 s.


  • Assume i(0) = 2 A.
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6.3 Inductors (5)
  • Example 6


  • Determine vc, iL, and the energy stored in the capacitor and inductor in the circuit of circuit shown below under dc conditions.
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6.4 Series and Parallel
 Inductors (1)
  • The equivalent inductance of series-connected inductors is the sum of the individual inductances.
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6.4 Series and Parallel
Inductors (2)
  • The equivalent capacitance of parallel inductors is the reciprocal of the sum of the reciprocals of the individual inductances.
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6.4 Series and Parallel
 Capacitors (3)
  • Example 7
  • Calculate the equivalent inductance for the inductive ladder network in the circuit          shown below:
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6.4 Series and Parallel
Capacitors (4)
  • Current and voltage relationship for R, L, C