electrical circuts analysis for electrical engineering students, Cheat Sheet of Electrical Circuit Analysis

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CHAPTER ONE

INTRODUCTION TO ELECTRICAL ENGINEERING

Electrical engineering is concerned with the conversion of energy from other forms into electrical energy, with the transmission and distribution of energy in electrical form, and with its control and reconversion for ultimate utilization. Electrical energy is not generally useful as an end in itself, it is converted into useful mechanical energy in motors, relays, and electromagnets; into heat energy in furnaces and ovens; into sound energy in loud speakers; into light energy; or into chemical energy in electrolytic processes. Electrical engineering is very closely associated with other professional branches. Mechanical engineers use the products of electrical engineering in the application and control of electric motors, as an integral part of power plants, and for remote metering and control, to mention only a few instances. Chemical engineers use the same products of process control, for heating and refrigeration, and automatic recording and indicating equipment. Civil and structural engineers are concerned with motor applications, electric power distribution within buildings, and stress and strain measurements. Aeronautical engineers deal with many essential applications for power production measurement, and control in aircraft and missiles. Chemical and physical scientists find electrical measuring devices to be valuable adjusts in their investigations. 1.1 BASIC ELECTRICAL QUANTITIES Before we are in the position to study the behavior of electrical systems and devices, we must first be familiar with the fundamental quantities used to express that behavior.

Electric Charge The most elemental quantity is electric charge, or quantity of electricity, just as volume of liquid may be considered elemental in hydraulic studies or displacement in mechanical studies. Charges may be positive (as in proton) or negative (as in electron). In MKS system, charge is measured in coulombs. For example, the charge on the electron is negative and equal to 1.602X

• 19 coulomb. The following points should be noted about electric charge: 1 - The coulomb is a large unit for charges. In 1 C of charge, there are 1 ( 1. 602 𝑋 10 − 19 ⁄ ) = 6. 24 𝑋 10 18 electrons. Thus realistic of laboratory values of charges are on the order of pC, nC, or C. 2 - According to experimental observations,the only charges that occur in nature are integral multiples of the electronic charge 𝑒 = − 1. 602 𝑥 10 − 19 𝐶. 3 - The law of conservation of charge states that can neither be created nor destroyed only transferred. Thus the algebraic sum of the electric charges in a system dos not change. Electrical Current

Potential Difference

Power and Energy

1.2 CIRCUIT ELEMENT

1.3 RESISTANCE AND OHM'S LAW

The relationship between current and voltage for a resistor is known ohm's law.

Fig. (1.3) (a) Short circuit (R=0) (b) Open circuit (R=)

1.4 NODES, BRANCHES, AND LOOPS

Fig. 1.4 Nodes, branches, and loops Fig. 1.5 The three-nods circuit

1.5 KIRCHHOFF'S LAWS

1.5.1 Kirchhoff's current law

(a) Origin circuit (b) Equivalent circuit Fig. 1.8 Current sources in parallel 1.5.2 Kirchhoff's voltage law

Fig. 1.9 A single-loop Fig. 1.10 Voltage sources in series Illustrating KVL (a) original circuit (b) equivalent circuit 1.6 SERIES AND PARALLEL CIRCUIT 1.6.1 Series circuit and voltages division

Fig. 1.11 A single-loop circuit with Fig. 1.12 Equivalent circuit of Two resistors in series. the Fig. 1.11 circuit.

1.6. 2 Parallel circuit and current division

• Fig. 1.13 Two resistor in parallel Fig. 1.14 Equivalent circuit for Fig. 1.

Example (1.1) Find V 3 and its polarity if the current I in the circuit of Fig. 1.15 is 0.4 A Fig. 1. Assume that V 3 has the same polarity as V 1. Applying KVL and starting from lower left corner. 𝑉 1 − 𝐼( 5. 0 ) − 𝑉 2 − 𝐼( 20. 0 ) + 𝑉 3 = 0

50. 0 − 2. 0 − 10. 0 − 8. 0 + 𝑉 3 = 0 𝑉 3 = − 30. 0 𝑉 Example (1.2) Find the equivalent resistance for the circuit shown in Fig. 1. Fig. 1. The two 20  resistors in parallel have an equivalent resistance: 𝑅𝑒𝑞 =

20 𝑥 20

20 + 20

= 10 

This is in series with 10  resistor so that their sum is 𝑅𝑒𝑞 1 = 10 + 10 = 20  This in turn is in parallel with the other 20  resistor so that the overall equivalent resistance is: 𝑅𝑜𝑣𝑒𝑟𝑎𝑙𝑙 𝑒𝑞 =

20 𝑥 20

20 + 20

= 10 

Example (1.2) Determine VO and i in the circuit shown in Fig. 1. Fig. 1. Example (1.3)

Example (1.4) Find the currents and voltages in the circuit shown in Fig. 1.19. Fig. 1.19

Example (1.5) Find Req for the circuit shown in Fig. 1.20. Fig. 1.20

Example (1.6) Calculate the equivalent resistance Rab in the circuit shown in Fig. 1.21. Fig. 1.21

Example (1.7) Fin the equivalent conductance Geq in the circuit shown in Fig. 1.22 (a).

Example For the circuit in figure below, find voltage v 1 and v 2. Example In the circuit shown in figure below, calculate i , the conductance G , and power P.