Alexander-Sadiku
Fundamentals of Electric Circuits

	Chapter 2
	Basic Laws

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.

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.

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:

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:

2.2 Nodes, Branches and Loops (2)

	Example 1

2.2 Nodes, Branches and Loops (3)

	Example 2

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.

2.3 Kirchhoff’s Laws (2)

	Example 4
	Determine the current I for the circuit shown in the figure below.

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.

2.3 Kirchhoff’s Laws (4)

	Example 5
	Applying the KVL equation for the circuit of the figure below.

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

"Example 3"

	Example 3

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:

"Example 4"

	Example 4

2.6 Wye-Delta Transformations