The impedance Z is a complex number that generalizes the concept of resistance to any circuit element as the proportionality constant between voltage and current V t Z I t The admittance Y of a circuit element is a complex number that is de ned to be the inverse of impedance Y 1 Z When circuit elements are connected in series the equivalent impedance is the sum of the individual impedances of each element Week 12 Day 2 AC Circuits Example ac voltage source current we need to determine I and Group Problem Inverse Addition and Multipication of Complex numbers What is the inverse of a complex number z x iy Consider two complex numbers z x iy and z x iy What is the sum z z What is the product z z Group Problem Modulus and Phase Consider two complex numbers For each complex number determine the modulus and phase Alternating Current Circuit Direct current dc current ows one way Alternating circuit ac current oscillates V t I t Complex Valued Functions for Voltage and Current Impedance Admittance Equivalent Impedance Circuit Elements in series Determining Amplitude and Phase from Equivalent impedance Write equivalent impedance in terms of modulus and phase Voltage across the branch and the current are related by Current phase equal phase of equivalent impedance Current amplitude AC Circuit Resistors AC Circuit Inductors Current and voltages are in phase 0 Group Problem Capacitors Calculate the impedance Z What is the modulus and phase constant for Z What is the amplitude of the current I What is the phase constant of the current Group Problem RL Circuit Calculate the equivalent impedance Z What is the modulus and phase constant for Z What is the amplitude of the current I What is the phase constant of the current Equivalent Admittance Circuit Elements in Parallel The voltage peaks earlier in time than the current by an amount t such that t 2 and 2 The equivalent admittance for circuit elements in parallel in the sum of the individual admittances Determining Amplitude and Phase from Equivalent Admittance Write equivalent admittance in terms of modulus and phase Current and voltage are related by Current phase equal negative phase of the equivalent admittance Current amplitude is Group Problem AC Parallel RLC Circuit Calculate the equivalent impedance Y What is the modulus and phase constant for Y What is the amplitude of the current What is phase constant of the current Concept Question Network reduction Correct answer 2 The equivalent impedance for the circuit elements is
View Full Document
Unlocking...