Eeng224 Circuit II, Course Information

1. Instructor:Huseyin Bilgekul, Room No: EE 207, Office Tel: 630 1333 • Office Hours:Monday 10.30-12.30, Wednesday 8:30-10:30 (Any time that I am present in the office) • Course Webpage: http://www.ee.emu.edu.tr/eeng224 • Lab Assistant: Sevki Kandulu • Textbook: C. K. Alexander and M. N. O. Sadiku, Electric Circuits, 3rd Edition, McGraw-Hill. • Grading: Midterm 1 Exam: % 20 Midterm 2 Exam: % 20 • Final Examination  : % 30 • HW & Quizzes       : % 15 • Lab Work             : % 15 • Prerequisite: EENG223 Circuit Theory I • NG Policy: NG grade will be given to students who do not attend more than 50% of the course lecture hours, miss the exams and fail. • Makeup Exams: Makeup exams will NOT be granted to students with less than 50% attendance. Eeng224 Circuit II, Course Information Huseyin Bilgekul EENG224 Circuit Theory II Department of Electrical and Electronic Engineering Eastern Mediterranean University

2. Chapter 9Sinusoids and Phasors Chapter Objectives: • Understand the concepts of sinusoids and phasors. • Apply phasors to circuit elements. • Introduce the concepts of impedance and admittance. • Learn about impedance combinations. • Apply what is learnt to phase-shifters and AC bridges. Huseyin BilgekulEENG224 Circuit Theory IIDepartment of Electrical and Electronic EngineeringEastern Mediterranean University

3. Alternating (AC) Waveforms • The term alternating indicates only that the waveform alternates between two prescribed levels in a set time sequence. • Instantaneous value: The magnitude of a waveform at any instant of time; denoted by the lowercase letters (v1, v2). • Peak amplitude: The maximum value of the waveform as measured from its average (or mean) value, denoted by the uppercase letters Vm. • Period (T): The time interval between successive repetitions of a periodic waveform. • Cycle: The portion of a waveform contained in one period of time. • Frequency: (Hertz) the number of cycles that occur in 1 s • The sinusoidal waveform is the only alternating waveform whose shape is unaffected by the response characteristics of R, L, and C elements. T

4. Sinusoids • The sinusoidal wave form can be derived from the length of the vertical projection of a radius vector rotating in a uniform circular motion about a fixed point. • The velocity with which the radius vector rotates about the center, called the angular velocity, can be determined from the following equation: • The angular velocity () is: • Since () is typically provided in radians per second, the angle αobtained using α = t is usually in radians. • The time required to complete one revolution is equal to the period (T) of the sinusoidal waveform. The radians subtended in this time interval are 2π.

5. Sinusoids • The basic mathematical format for the sinusoidal waveform is: Vmsinα • Vm is the peak value of the waveform and α is the unit of measure for the horizontal axis. • The equationα = t states that the angle α through which the rotating vector will pass is determined by the angular velocity of the rotating vector and the length of time the vector rotates. • For a particular angular velocity (fixed ), the longer the radius vector is permitted to rotate (that is, the greater the value of t ), the greater will be the number of degrees or radians through which the vector will pass.The general format of a sine wave can also be as:

6. Sinusoids T Period • A SINUSOID is a signal that has the form of the sine or cosine function. • The sinusoidal current is referred to as AC. Circuits driven by AC sources are referred to as AC Circuits. • Sketch of Vmsint. (a)As a function of t. (b)As a function of t . • Vm is the AMPLITUDE of the sinusoid. • is the ANGULAR FREQUENCY in radians/s. • f is the FREQUENCY in Hertz. • T is the period in seconds.

7. Phase of Sinusoids • A periodic function is one that satisfies v(t) = v(t + nT), for all t and for all integers n. • Only two sinusoidal values with the same frequency can be compared by their amplitude and phase difference. • If phase difference is zero, they are in phase; if phase difference is not zero, they are out of phase.

8. Phase of Sinusoids • The terms lead and lag are used to indicate the relationship between two sinusoidal waveforms of the same frequency plotted on the same set of axes. • The cosine curve is said to lead the sine curve by 90°. • The sine curve is said to lag the cosine curve by 90°. • 90 is referred to as the phase angle between the two waveforms. • When determining the phase measurement we first note that each sinusoidal function has the same frequency, permitting the use of either waveform to determine the period. • Since the full period represents a cycle of 360°, the following ratio can be formed:

9. Phase of Sinusoids • Consider the sinusoidal voltage having phase φ, • v2 LEADS v1 by phase φ. • v1 LAGS v2 by phase φ. • v1 and v2 are out of phase.

10. (120 V at 60 Hz) versus (220 V at 50 Hz) AC • In North and South America the most common available ac supply is 120 V at 60 Hz, while in Europe and the Eastern countries it is 220 V at 50 Hz. • Technically there is no noticeable difference between 50 and 60 cycles per second (Hz). • The effect of frequency on the size of transformers and the role it plays in the generation and distribution of power was also a factor. • The fundamental equation for transformer design is that the size of the transformer is inversely proportional to frequency. • A 50 HZ transformer must be larger than a 60 Hz (17% larger) sinusoidal voltage having phase φ. • Higher frequencies result in concerns about arcing, increased losses in the transformer core due to eddy current andhysteresis losses, and skin effect phenomena. • Larger voltages (such as 220 V) raise safety issues beyond those of 120 V. • Higher voltages result in lower current for the same demand, permitting the use of smaller conductors. • Motors and power supplies, found in common home appliances and throughout the industrial community, can be smaller in size if supplied with a higher voltage.

11. Trigonometric Identities • Sine and cosine form conversions. Graphically relating sine and cosine functions.

12. Figure shows a pair of waveforms v1 and v2 on an oscilloscope. Each major vertical division represents 20 V and each major division on the horizontal (time) scale represents 20 ms. Voltage v1 leads. Prepare a phasor diagram using v1 as reference. Determine equations for both voltages.

13. EXERCISE • Voltage and current are out of phase by 40°, and voltage lags. Using current as the reference, sketch the phasor diagram and the corresponding waveforms.