1. FUNDAMENTALS OF ELECTRICAL ENGINEERING [ ENT 163 ]
LECTURE #2
BASIC LAWS
HASIMAH ALI
Programme of Mechatronics,
School of Mechatronics Engineering, UniMAP.

2. CONTENTS Introduction Ohm’s Law Nodes, Branches and Loops
Kirchhoff’s Laws
Series Resistors and Voltage Division
Parallel Resistors and current Division

3. Introduction Fundamental laws – govern electric circuits:
Ohm’s Law
Kirchhoff’s law
Technique commonly applied:
Resistors in series/ parallel
Voltage division
Current division
Delta-to-wye and wye-to-delta transformations

4. Ohm’s Law Resistance: ability to resist current (R) .
Materials in general have a characteristics behavior of resisting the flow of electric charge.
Resistance: ability to resist current (R) .
Material
Resistitivity( )
Usage
Silver
1.64 x 10-8
Conductor
Copper
1.72 x 10-8
Aluminum
2.8 x 10-8
Gold
2.45 x 10-8
Carbon
4 x 10-5
Semiconductor
Germanium
47 x 10-2
Silicon
6.4 x 102
Paper
1010
Insulator
Mia
5 x 1011
Glass
1012
Teflon
3 x 1012

5. Ohm’s Law
Resistor: circuit element that used to model the current – resisting behavior.
Relationship between current and voltage for a resistor Ohm’s law
Ohm’s law states that the voltage v across a resistor is directly proportionally to the current i flowing through the resistor.
Georg Simon Ohm (1787 – 1854), a German physicist, is credited with finding the relationship between current and voltage for a resistor.
Ohm- defined the constant of proportionality for a resistor resistance, R
Resistance, R: denotes its ability to resist the flow of electric current(Ω)
The two extreme possible values of R:
R= 0 is called a short circuit (v= i R=0)
R=∞ is called open circuit

6. Ohm’s Law
A short circuit is a circuit element with resistance approaching zero
An open circuit is a circuit element with resistance approaching infinity.
Resistor is either fixed or variable.
Fixed resistors have constant resistor.
The two common types of fixed resistors:
Wire wound
Composition
Variable resistor have adjustable resistance. Example potentiometer.
Reciprocal of resistance, known as conductance, G:
The conductance is the ability of an element to conduct electric current , it is measured in mhos or Siemens (S).

7. Ohm’s Law The power is dissipated by a resistor is expressed by: or
Note:
The power dissipated in a resistor is a nonlinear function of either current or voltage.
Since R and G are positive quantities, the power dissipated in a resistor is always positive( resistor- absorbs power from circuit. Thus resistor is a passive element, incapable of generating energy.

8. Nodes, Branches and Loops
A network – interconnection of elements or devices.
A circuit – network providing one/ more closed paths.
Branch represents a single elements such as a voltage source or resistor. A branch represents any two-terminal element.
Node is the point of connection between two or more branches.
It usually indicated by a dot in a circuit.
Loop is any closed path in a circuit ; formed by starting at a node, passing through a set of nodes, and returning to the starting node without passing through ant node more than once. 5Ω b
10 V + - 2A 2Ω 3Ω a c

9. Nodes, Branches and Loops
Two or more elements are in series if they exclusively share a single node and consequently carry the same current.
Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.

10. Nodes, Branches and Loops
Example:
Determine the number of branches and nodes in the circuit shown in Figure Identify which elements are in series and which are in parallel.
10 V + - 2A 6Ω 5Ω
Figure 2.12

11. Kirchhoff’s Law
First introduced in 1874 by the German physicist Gustav Robert Kirchhoff ( )
Kirchhoff’s current law (KCL):
The algebraic sum of currents entering a node (or close boundary) is zero.
The sum of the currents entering a node is equal to the sum of the currents leaving the node. i1 i2 i3 i4 i5
Fig: Currents at a node illustrating KCL

12. Kirchhoff’s Law IT I1 I2 I3 a b IT a = b

13. Kirchhoff’s Law Kirchhoff’s voltage law (KVL):
The algebraic sum of all voltages around a closed path (or loop) is zero.
2. Sum of voltage drops is equal to sum of voltage rises. + - v2 v1 v5 v3 v4
Sum of voltage drop = Sum of voltage rises

14. Kirchhoff’s Law Kirchhoff’s voltage law (KVL): V3 + - V2 V1 Vab = Vab

15. Kirchhoff’s Law Example:
For the circuit in Fig find voltages v1 and v2. - +
20V v1 v2 2Ω 3 Ω

16. Kirchhoff’s Law Problem: Find v1and v2 in the circuit of the Fig. 4Ω -+
10V v1 8V 2Ω v2

17. Kirchhoff’s Law Problem: Determine voand i in the circuit of the Fig.4Ω - +
12V v1 4V 6Ω vo
2vo i

18. Kirchhoff’s Law Problem:
Find current io and voltage vo in the circuit shown in Fig. below. 4Ω a vo + - io 3A
0.5io

19. Series Resistors and Voltage Division
Consider a single-loop circuit with two resistors in series v1 + - v v2 a b R1 R2 i
Applying Ohm’s law of each resistor
(1)
If apply KVL to the loop (CW), we have
(2) i v
Combing (1) and (2): - + a - + v
Req or b

20. Series Resistors and Voltage Division
The equivalent resistance of any number of resistors connected in series is the sum of the individual resistances.
Mathematically,
To determine the voltage across each resistor shown in Fig,
Principle of voltage division:

21. Parallel Resistors And Current Division
The equivalent resistance of two parallel resistors is equal to the product of their resistances divided by their sum.
Mathematically,
For a circuit with N resistors in parallel,

22. Parallel Resistors And Current Division
Consider the circuit below where two resistors are connected in parallel and therefore have the same voltage across them. From Ohm’s law R1
Node a i1 i2 R2
Node b - + v i
(3)
Applying KCL at node a gives
(4),
Substitute (3) into (4), we get
For a circuit with N resistors in parallel,

23. Parallel Resistors And Current Division
Principle of current division:
Extreme cases:
R2=0,-Req=0 ; entire current flows through the short circuit.
R2= ∞ , Req=R1; current flows through the path of least resistance.

24. Wye – Delta Transformation
Implementation – three – phase networks, electrical filters, etc.
Delta to wye conversion: each resistor in the Y network is the product of the resistors in the two adjacent ∆ branches, divided by the sum of the three ∆ resistors.

25. Wye – Delta Transformations
Wye to delta conversion: each resistor in the network is the sum of all possible products of Y resistors taken two at a time, divided by the opposite Y resistor.

26. Wye – Delta Transformations
Y and ∆ networks are said to be balanced when
Therefore conversion formulas: