Thevenin's and Norton's Theorems: Simplifying Complex Circuits, Lecture notes of Physics Fundamentals

Download Thevenin's and Norton's Theorems: Simplifying Complex Circuits and more Lecture notes Physics Fundamentals in PDF only on Docsity! LECTURE # Thevenin’s Theorem is a network analysis procedure meant to simplify the computations of a complex network (with several sources and resistances). It does so by reducing a complex network to simple equivalent circuit (Thevenin’s Equivalent Circuit) containing a Single Voltage Source in series with a two Resistances. Whereby: The voltage source is the open circuit voltage measured between terminals where its required to determine the current One of the resistors is the Thevenin’s equivalent resistance, measured between terminals (where its required to compute current) in a passive circuit While the other resistance represents the load resistance (connected between terminals where its required to find current). Thevenin’ s Theorem   Active Network with linear Sources and Resistances resistance Rth   𝐴  𝐵  𝑹𝑳  𝑬𝒕𝒉  𝑨  𝑹𝒕𝒉  Equivalent Source, then its possible to determine the Load current, i.e. current between terminals A & B   𝐸 h𝑡h −𝑇h𝑒𝑣𝑒𝑛𝑖𝑛′ 𝑠𝑉𝑜𝑙𝑡h𝑎𝑔𝑒    𝑇h𝑒𝑣𝑒𝑛𝑖𝑛′ 𝑠𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡h 𝑆𝑜𝑢𝑟𝑐𝑒  𝑰 𝑳  𝑹𝑳  𝑩  𝑹𝑳−𝑹𝒆𝒔𝒊𝒔𝒕𝒂𝒏𝒄𝒆𝒐𝒇 𝒕𝒉𝒆𝒃𝒓𝒂𝒏𝒄𝒉𝒘𝒉𝒆𝒓𝒆𝒊𝒕𝒔 𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝒕𝒐𝒅𝒆𝒕𝒆𝒓𝒎𝒊𝒏𝒆𝒄𝒖𝒓𝒓𝒆𝒏𝒕  Example # 𝐸  𝑅1  𝐷𝑒𝑡h𝑒𝑟𝑚𝑖𝑛𝑒𝑐𝑢𝑟𝑟𝑒𝑛𝑡h h𝑡hh𝑟𝑜𝑢𝑔 𝑟𝑒𝑠𝑖𝑠𝑡h𝑎𝑛𝑐𝑒𝑅2𝑢𝑠𝑖𝑛𝑔𝑇h𝑒𝑣𝑒𝑛𝑖𝑛 ′ 𝑠𝑇h𝑒𝑜𝑟𝑒𝑚  𝑹𝟑 𝑹𝟐  𝑅1=4Ω  𝑅2=8Ω  𝑟 𝑖=1Ω  𝑅3=6Ω  𝐸=24𝑉  𝑹𝟒  𝐷𝑒𝑡h𝑒𝑟𝑚𝑖𝑛𝑒𝑐𝑢𝑟𝑟𝑒𝑛𝑡h h𝑡hh𝑟𝑜𝑢𝑔 𝑟𝑒𝑠𝑖𝑠𝑡h𝑎𝑛𝑐𝑒𝑅2𝑢𝑠𝑖𝑛𝑔𝑇h𝑒𝑣𝑒𝑛𝑖𝑛 ′ 𝑠𝑇h𝑒𝑜𝑟𝑒𝑚  LECTURE # Norton’s Theorem 𝑰 𝑳  𝑬  𝑹𝟑  𝑹𝟒  𝑹𝟓  𝑹𝟔  𝑹𝟏  𝑹𝟐  𝑰 𝑨  𝑹𝟐=𝑹𝟒=𝑹𝟔=𝟒Ω 𝑹𝟏=∞Ω  𝑹𝟑=𝟔Ω  𝑹𝟓=𝟐Ω  𝑬=𝟒𝟎𝑽  𝑰 𝑨=𝟖 𝑨  Example # V3=? R1 IA E1 R3 R2 R4 𝑹𝟏=𝑹𝟒=𝟐Ω  𝑹𝟐=𝟒Ω,𝑹𝟒=𝟑Ω  𝑬𝟏=𝟏𝟔𝑽 𝑰 𝑨=𝟖 𝑨  Example # 2 𝐸  𝑅1  𝐷𝑒𝑡h𝑒𝑟𝑚𝑖𝑛𝑒𝑐𝑢𝑟𝑟𝑒𝑛𝑡h h𝑡hh𝑟𝑜𝑢𝑔 𝑟𝑒𝑠𝑖𝑠𝑡h𝑎𝑛𝑐𝑒𝑅2𝑢𝑠𝑖𝑛𝑔𝑁𝑜𝑟𝑡h𝑜𝑛′ 𝑠𝑇h𝑒𝑜𝑟𝑒𝑚  𝑹𝟑 𝑹𝟐  𝑅1=4Ω  𝑅2=8Ω  𝑟 𝑖=1Ω  𝑅3=6Ω  𝐸=24𝑉  𝑹𝟒  𝐷𝑒𝑡h𝑒𝑟𝑚𝑖𝑛𝑒𝑐𝑢𝑟𝑟𝑒𝑛𝑡h h𝑡hh𝑟𝑜𝑢𝑔 𝑟𝑒𝑠𝑖𝑠𝑡h𝑎𝑛𝑐𝑒𝑅2𝑢𝑠𝑖𝑛𝑔𝑁𝑜𝑟𝑡h𝑜𝑛′ 𝑠𝑇h𝑒𝑜𝑟𝑒𝑚  𝑅4=6Ω  Example # R1 R4 𝑹𝟏=𝑹3=𝟐Ω  𝑹𝟐=𝟒Ω,𝑹𝟒=𝟑Ω  𝑬𝟏=𝟏𝟔𝑽 𝑰 𝑨=𝟖 𝑨  R3 R2 E1 V4=? 𝒓=𝟏Ω  Example # 𝑹𝟏=𝑹𝟑=𝟐Ω  𝑹𝟐=𝟒Ω,𝑹𝟒=𝟑Ω  𝑰 𝑨=𝟖 𝑨  R1 R3 R2 R4IA V4=? 𝑰 𝒔𝒄  𝑹𝑵  𝑰 𝑳