1. Supplement to Circuits Analysis
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2. Outline
Basic Concepts
Basic laws
Useful theorems
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3. Basic Concepts Current, voltage and power Sources Ohm’s law
Independent sources
Controlled sources
Ohm’s law
Kirchhoff’s current and voltage laws
Passive elements
Resistor R
Capacitor C
Inductor L
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4. Current Direction and value Constant value and instantaneous value
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5. Current Two different methods of labeling the same current.
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6. Current (a,b) Inadequate definitions of a current.
(c) the correct definition of i1(t).
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7. Voltage
Voltage across a terminal pair is a measure of the work required to move charge through the element.
Voltage can exist between a pair of terminals whether a current is flowing or not.
Distinguish between energy supplied to or by the element.
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8. Voltage (a, b) These are inadequate definitions of a voltage.
(c) A correct definition includes both a symbol for the variable and a plus-minus symbol pair.
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9. Voltage (a,b) Terminal B is 5 V positive with respect to terminal A;
(c,d) terminal A is 5 V positive with respect to terminal B.
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10. Power
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11. Power
If the current arrow is directed into the “ +” marked terminal of an element, then p = vi yields the absorbed power. A negative value indicates that power is actually being generated by the element.
If the current arrow is directed out of the “ +” terminal of an element, then p = vi yields the supplied power. A negative value in this case indicates that power is actually being absorbed instead of generated.
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12. Power Find the power absorbed by each element in the circuit below.
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13. Sources Independent sources Controlled sources Voltage source
Current source
Controlled sources
Voltage-controlled current source (VCCS)
Voltage-controlled voltage source (VCVS)
Current-controlled current source (CCCS)
Current-controlled voltage source (CCVS)
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14. Independent Voltage Source
Symbol for:
(a) DC voltage source
(b) Battery
(c) ac voltage source
An independent voltage source is characterized by a terminal voltage which is completely independent of the current through it.
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15. independent Current Source
Symbol for an independent current source.
Current source can deliver infinite power from its terminals, because it produces the same finite current for any voltage across it, no matter how large the voltage may be.
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16. Controlled Sources (a) current-controlled current source;
(b) voltage-controlled current source;
(c) voltage-controlled voltage source;
(d) current-controlled voltage source.
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17. Controlled Sources
In the circuit below ,if v2 is known to be 3 V, find vL .
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18. Ohm’s law
v = i R or
i =
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19. Ohm’s law
Conductance
Absorbed power
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20. Nodes, Paths, Loops, and Branches
A point at which two or more elements have a common connection is called a node.
If no node is encountered more than once, then the set of nodes and elements that we have passed through is defined as a path.
If the node at which we started is the same as the node on which we ended, then the path is, by definition, a closed path or loop.
We define a branch as a single path in a network, composed of one simple element and node at each end of the element.
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21. Nodes, Paths, Loops, and Branches
A circuit containing three nodes and five branches.
(b) Node 1 is redrawn to look like two nodes; it is still one node.
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22. Kirchhoff’s Current Law
The algebraic sum of the currents entering any node is zero.
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23. Kirchhoff’s Current Law
Figure 3.2
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24. Kirchhoff’s Voltage Law
The algebraic sum of the voltages around any closed path is zero.
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25. The Single Loop Circuit
Simple resistive circuit.
All the element in a circuit that carry the same current are said to be connected in series.
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26. The Single Loop Circuit
Simple resistive circuit.
All the element in a circuit that carry the same current are said to be connected in series.
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27. The Single Node-pair Circuit
Simple resistive circuit.
Elements in a circuit hacing a common voltage across them are said to be connected in parallel.
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28. Resistor Series combination of N resistors.
(b) Electrically equivalent circuit.
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29. Resistor
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30. Resistor A circuit with N resistors in parallel. Equivalent circuit.
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31. Resistor Beginning with a simple KCL equation, or Thus,
A special case worth remembering is
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32. Electrical symbol and current-voltage conventions for a capacitor.
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33. Capacitor
(c)
(d)
N capacitors connected in series; (b) equivalent circuit; (c) N capacitors connected in parallel; (d) equivalent circuit to (c).
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34. Inductor
Electrical symbol and current-voltage conventions for an inductor.
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35. Inductor N inductors connected in series; Equivalent circuit;
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36. Inductor (c) N inductors connected in parallel;
(d) equivalent circuit for circuit in (c).
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37. Voltage Division We may find v2 by applying KVL and Ohm’s law: so
Thus,
An illustration of voltage division. or
For a string of N series resistors, we may write:
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38. Voltage Division
Use voltage division to determine vx in the adjacent circuit.
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39. Current Division
The current flowing through R2 is or
For a parallel combination of N resistors, the current through Rk is
An illustration of
current division.
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40. Current Division Determine the current Ix if I1 = 100 mA.
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41. Thévenin’s Theorem.
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42. Norton’s Theorem.
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43. Thévenin’s Theorem Application
Determine the Thévenin and Norton Equivalents of Network A in (a).
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44. Thévenin’s Theorem Application
Thévenin’s theorem applied to simplify the circuit of (a) to that in (b).
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45. The Source-Absorption Theorem.
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46. The Source-Absorption Theorem.
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