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Alexander-Sadiku
Fundamentals of Electric Circuits
  • Chapter 2
  • Basic Laws
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Basic Laws - Chapter 2
  • 2.1  Ohm’s Law.
  • 2.2  Nodes, Branches, and Loops.
  • 2.3  Kirchhoff’s Laws.
  • 2.4  Series Resistors and Voltage Division.
  • 2.5  Parallel Resistors and Current Division.
  • 2.6  Wye-Delta Transformations.
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2.1 Ohms Law (1)
  • Ohm’s law states that the voltage across a resistor is directly proportional to the current I flowing through the resistor.


  • Mathematical expression for Ohm’s Law  is as follows:



  • Two extreme possible values of R:              0 (zero)  and ¥ (infinite) are related with two basic circuit concepts: short circuit and open circuit.
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2.1 Ohms Law (2)
  • Conductance is the ability of an element to conduct electric current; it is the reciprocal       of resistance R and is measured in mhos or siemens.



  • The power dissipated by a resistor:
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2.2 Nodes, Branches and Loops (1)
  • A branch represents a single element such as a voltage source or a resistor.
  • A node is the point of connection between two   or more branches.
  • A loop is any closed path in a circuit.


  • A network with b branches, n nodes, and l independent loops will satisfy the fundamental theorem of network topology:
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2.2 Nodes, Branches and Loops (2)
  • Example 1
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2.2 Nodes, Branches and Loops (3)
  • Example 2
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2.3 Kirchhoff’s Laws (1)
  • Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node      (or a closed boundary) is zero.
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2.3 Kirchhoff’s Laws (2)
  • Example 4


  • Determine the current I for the circuit shown in the figure below.
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2.3 Kirchhoff’s Laws (3)
  • Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero.
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2.3 Kirchhoff’s Laws (4)
  • Example 5


  • Applying the KVL equation for the circuit of the figure below.
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2.4 Series Resistors and Voltage Division (1)
  • Series: Two or more elements are in series if they are cascaded or connected sequentially                     and consequently carry the same current.


  • The equivalent resistance of any number of resistors connected in a series is the sum of the  individual resistances.



  • The voltage divider can be expressed as
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"Example 3"
  • Example 3
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2.5 Parallel Resistors and Current Division (1)
  • Parallel: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.


  • The equivalent resistance of a circuit with             N resistors in parallel is:



  • The total current i is shared by the resistors in inverse proportion to their resistances. The current divider can be expressed as:
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"Example 4"
  • Example 4
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2.6 Wye-Delta Transformations