ECE21116 Electric Circuit Theory 2 PDF

ECE21116 ELECTRIC CIRCUIT THEORY 2 AC vs DC SOURCES OUTPUT BEHAVIOR OF PASSIVE ELEMENTS AC DC PHASORS A phasor is a complex number that represents the amplitude and phase of a sinusoid. COMPLEX NUMBERS A complex number z can be written in the following forms: 𝑧𝑧 = 𝑥𝑥 + 𝑗𝑗𝑗...

ECE21116 ELECTRIC CIRCUIT THEORY 2 AC vs DC SOURCES OUTPUT BEHAVIOR OF PASSIVE ELEMENTS AC DC PHASORS A phasor is a complex number that represents the amplitude and phase of a sinusoid. COMPLEX NUMBERS A complex number z can be written in the following forms: 𝑧𝑧 = 𝑥𝑥 + 𝑗𝑗𝑗𝑗 Rectangular form 𝑧𝑧 = 𝑟𝑟∠𝜙𝜙 Polar form 𝑧𝑧 = 𝑟𝑟𝑟𝑟 𝑗𝑗𝜙𝜙 Exponential form SINUSOID-PHASOR TRANSFORMATION Time-Domain Representation Phasor-Domain Representation 𝑉𝑉𝑚𝑚 𝑐𝑐𝑐𝑐𝑐𝑐(𝜔𝜔𝑡𝑡 + 𝜙𝜙) 𝑉𝑉𝑚𝑚 ∠𝜙𝜙 𝑉𝑉𝑚𝑚 𝑠𝑠𝑠𝑠𝑠𝑠(𝜔𝜔𝑡𝑡 + 𝜙𝜙) 𝑉𝑉𝑚𝑚 ∠(𝜙𝜙 − 90°) 𝐼𝐼𝑚𝑚 𝑐𝑐𝑐𝑐𝑐𝑐(𝜔𝜔𝑡𝑡 + 𝜃𝜃) 𝐼𝐼𝑚𝑚 ∠𝜃𝜃 𝐼𝐼𝑚𝑚 𝑠𝑠𝑠𝑠𝑠𝑠(𝜔𝜔𝑡𝑡 + 𝜃𝜃) 𝐼𝐼𝑚𝑚 ∠(𝜃𝜃 − 90°) QUESTION What is the phasor form of 𝑣𝑣 𝑡𝑡 = 45sin(30𝑡𝑡 + 50°)? A) 45∠30° B) 45∠50° C) 45∠ − 40° D) 45∠130° ALTERNATING WAVEFORMS GENERATION FARADAY’s LAW 𝑑𝑑∅ 𝐸𝐸 = 𝑁𝑁 𝑑𝑑𝑑𝑑 SINUSOIDAL AC VOLTAGE SINUSOIDAL AC VOLTAGE Waveform: The path traced by a quantity plotted as a function of some variable such as time, position, degrees, radians, temperature, and so on. SINUSOIDAL AC VOLTAGE Instantaneous value: The magnitude of a waveform at any instant of time; denoted by lowercase letters (e1, e2). SINUSOIDAL AC VOLTAGE Peak amplitude: The maximum value of a waveform as measured from its average, or mean value (Em) SINUSOIDAL AC VOLTAGE Peak value: The maximum instantaneous value of a function as measured from the zero-volt level. SINUSOIDAL AC VOLTAGE Peak-to-peak value: Full voltage between positive and negative peaks of the waveform, that is, the sum of the magnitude of the positive and negative peaks (Ep-p). SINUSOIDAL AC VOLTAGE Periodic waveform: A waveform that continually repeats itself after the same time interval. SINUSOIDAL AC VOLTAGE Period (T): The time interval between successive repetitions of a periodic waveform SINUSOIDAL AC VOLTAGE Cycle: The portion of a waveform contained in one period of time. SINUSOIDAL AC VOLTAGE Frequency ( f): The number of cycles that occur in 1 s. FREQUENCY The unit of measure for frequency is the hertz (Hz), where EXAMPLE Find the period of a periodic waveform with a frequency of: a. 60 Hz b. 1000 Hz  Prepared by Engr. John Paul Timola, LPT Reference: Introductory Circuit Analysis by Robert Boylestad