Alexander-Sadiku
Fundamentals of Electric Circuits
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Chapter 6 |
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Capacitors and Inductors |
Capacitors and Inductors Chapter
6
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6.1 Capacitors |
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6.2 Series and Parallel Capacitors |
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6.3 Inductors |
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6.4 Series and Parallel Inductors |
6.1 Capacitors (1)
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A capacitor is a passive element
designed to store energy in its electric
field. |
6.1 Capacitors (2)
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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). |
6.1 Capacitors (3)
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If i is flowing into the +ve terminal
of C |
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Charging => i is +ve |
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Discharging => i is –ve |
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6.1 Capacitors (4)
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The energy, w, stored in the capacitor
is |
6.1 Capacitors (5)
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Example 1 |
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The current through a 100-mF capacitor is |
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i(t) = 50 sin(120 pt) mA. |
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Calculate the voltage across it at t =1
ms and |
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t = 5 ms. |
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Take v(0) =0. |
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6.1 Capacitors (6)
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Example 2 |
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An initially uncharged 1-mF capacitor
has the current shown below across it. |
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Calculate the voltage across it at t =
2 ms and |
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t = 5 ms. |
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6.2 Series and Parallel
Capacitors (1)
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The equivalent capacitance of N parallel-connected
capacitors is the sum of the individual capacitances. |
6.2 Series and
Parallel
Capacitors (2)
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The equivalent capacitance of N series-connected
capacitors is the reciprocal of the sum of the reciprocals of the individual
capacitances. |
6.2 Series and Parallel
Capacitors (3)
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Example 3 |
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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)
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Example 4 |
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Find the voltage across each of the
capacitors in the circuit shown below: |
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6.3 Inductors (1)
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An inductor is a passive element
designed to store energy in its
magnetic field. |
6.3 Inductors (2)
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Inductance is the property whereby an
inductor exhibits opposition to the change of current flowing through it,
measured in henrys (H). |
6.3 Inductors (3)
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The current-voltage relationship of an
inductor: |
6.3 Inductors (4)
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Example 5 |
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The terminal voltage of a 2-H inductor is |
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v = 10(1-t) V |
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Find the current flowing through it at t = 4 s and the energy stored in it
within 0 < t < 4 s. |
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Assume i(0) = 2 A. |
6.3 Inductors (5)
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Example 6 |
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Determine vc, iL,
and the energy stored in the capacitor and inductor in the circuit of circuit
shown below under dc conditions. |
6.4 Series and
Parallel
Inductors (1)
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The equivalent inductance of series-connected
inductors is the sum of the individual inductances. |
6.4 Series and Parallel
Inductors (2)
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The equivalent capacitance of parallel
inductors is the reciprocal of the sum of the reciprocals of the individual
inductances. |
6.4 Series and
Parallel
Capacitors (3)
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Example 7 |
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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)
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Current and voltage relationship for R,
L, C |
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