Schedule Date Day Class No. Ttle Chapters HW Due date Lab Due date 8 Sept Mon Krchoff s Laws..3 NO LAB Exam 9 Sept Tue NO LAB 10 Sept Wed 3 Power.4.5 11 Sept Thu NO LAB 1 Sept Fr Rectaton HW 1 13 Sept Sat 14 Sept Sun 15 Sept Mon 4 Ohm s Law.5.6 16 Sept Tue LAB 1 ECEN 301 Dscusson # Krchhoff s Laws 1
Dne Source Neph 5:6 6 And we talk of Chrst, we rejoce n Chrst, we preach of Chrst, we prophesy of Chrst, and we wrte accordng to our propheces, that our chldren may know to what source they may look for a remsson of ther sns. ECEN 301 Dscusson # Krchhoff s Laws
Lecture Krchhoff s Current and Voltage Laws ECEN 301 Dscusson # Krchhoff s Laws 3
Charge Elektron: Greek word for amber ~600 B.C. t was dscoered that statc charge on a pece of amber could attract lght objects (feathers) Charge (q): fundamental electrc quantty Smallest amount of charge s that carred by an electron/proton (elementary charges): q e / q p / 1.60 10 19 C Coulomb (C): basc unt of charge. ECEN 301 Dscusson # Krchhoff s Laws 4
Electrc Current Electrc current (): the rate of change (n tme) of charge passng through a predetermned area (IE the cross-sectonal area of a wre). Analogous to olume flow rate n hydraulcs Current () refers to q (dq) unts of charge that flow through a crosssectonal area (Area) n t (dt) unts of tme q t dq dt A Area Ampere (A): electrc current unt. 1 ampere = 1 coulomb/second (C/s) Poste current flow s n the drecton of poste charges (the opposte drecton of the actual electron moement) ECEN 301 Dscusson # Krchhoff s Laws 5
Charge and Current Example For a metal wre, fnd: The total charge (q) The current flowng n the wre () Gen Data: wre length = 1m wre dameter = x 10-3 m charge densty = n = 10 9 carrers/m 3 charge of an electron = q e = -1.60 x 10-19 charge carrer elocty = u = 19.9 x 10-6 m/s ECEN 301 Dscusson # Krchhoff s Laws 6
Charge and Current Example For a metal wre, fnd: The total charge (q) The current flowng n the wre () Gen Data: wre length = 1m wre dameter = x 10-3 m charge densty = n = 10 9 carrers/m 3 charge of an electron = q e = -1.60 x 10-19 charge carrer elocty = u = 19.9 x 10-6 m/s Volume length area Number of carrers olume carrer densty L r (1m ) 10 3 m N V n 10 10 3 6 m 3 10 carrers 9 carrers 3 m 10 6 m 3 ECEN 301 Dscusson # Krchhoff s Laws 7
Charge and Current Example For a metal wre, fnd: The total charge (q) The current flowng n the wre () Gen Data: wre length = 1m wre dameter = x 10-3 m charge densty = n = 10 9 carrers/m 3 charge of an electron = q e = -1.60 x 10-19 charge carrer elocty = u = 19.9 x 10-6 m/s Charge number of carrers charge/carrer q N q e 10 3 carrers 1.60 10 19 C / carrer 50.33 10 3 C ECEN 301 Dscusson # Krchhoff s Laws 8
Charge and Current Example For a metal wre, fnd: The total charge (q) The current flowng n the wre () Gen Data: wre length = 1m wre dameter = x 10-3 m charge densty = n = 10 9 carrers/m 3 charge of an electron = q e = -1.60 x 10-19 charge carrer elocty = u = 19.9 x 10-6 m/s Current carrer charge densty q L 1A ( C / m) 50.33 10 3 u( m / s) C / m 19.9 per unt 10 6 length m / s carrer elocty ECEN 301 Dscusson # Krchhoff s Laws 9
Krchhoff s Current Law (KCL) KCL: charge must be consered the sum of the currents at a node must equal zero. Node 1 n N 1 n 0 1.5 V 1 3 At Node 1: - 1 3 = 0 OR: - 1 - - 3 = 0 NB: a crcut must be CLOSED n order for current to flow ECEN 301 Dscusson # Krchhoff s Laws 10
Krchhoff s Current Law (KCL) Potental problem of too many branches on a sngle node: not enough current gettng to a branch Node 1 1.5 V 1 3 4 5 6 Suppose: all lghts hae the same resstance 4 needs 1A What must the alue of be? ECEN 301 Dscusson # Krchhoff s Laws 11
Krchhoff s Current Law (KCL) Potental problem of too many branches on a sngle node: not enough current gettng to a branch Node 1-1 3 4 5 6 = 0 1.5 V 1 3 4 5 6 BUT: snce all resstances are the same: 1 = = 3 = 4 = 5 = 6 = n - 6 n = 0 6 n = 6(1A) = = 6A ECEN 301 Dscusson # Krchhoff s Laws 1
Krchhoff s Current Law (KCL) Example1: fnd 0 and 4 s = 5A, 1 = A, = -3A, 3 = 1.5A 0 1 s V s 3 4 ECEN 301 Dscusson # Krchhoff s Laws 13
Krchhoff s Current Law (KCL) Example1: fnd 0 and 4 s = 5A, 1 = A, = -3A, 3 = 1.5A Node a 0 1 s V s Node b 3 4 NB: Frst thng to do decde on unknown current drectons. If you select the wrong drecton t won t matter a negate current ndcates current s flowng n the opposte drecton. Must be consstent Once a current drecton s chosen must keep t Node c ECEN 301 Dscusson # Krchhoff s Laws 14
Krchhoff s Current Law (KCL) Example1: fnd 0 and 4 s = 5A, 1 = A, = -3A, 3 = 1.5A Node a 0 1 s V s Node b 3 4 Fnd 0 at Node a : 0 1 0 0 1 3 1A Fnd 4 at Node c : 4 s 3 4 0 3 s 1.5 5 3.5A Node c ECEN 301 Dscusson # Krchhoff s Laws 15
Krchhoff s Current Law (KCL) Example: usng KCL fnd s1 and s 3 = A, 5 = 0A, = 3A, 4 = 1A s s1 R V s V s1 4 R 4 R 3 3 5 R 5 ECEN 301 Dscusson # Krchhoff s Laws 16
Krchhoff s Current Law (KCL) Example: usng KCL fnd s1 and s 3 = A, 5 = 0A, = 3A, 4 = 1A V s1 s1 R R 3 s R 4 4 Supernode R 5 V s KCL at supernode : 3 5 A s1 3 5 s1 0 3 5 0 ECEN 301 Dscusson # Krchhoff s Laws 17
Krchhoff s Current Law (KCL) Example: usng KCL fnd s1 and s 3 = A, 5 = 0A, = 3A, 4 = 1A V s1 R Node a s1 R 3 s R 4 4 3 5 R 5 V s KCL at Node a : s s1 s 0 3 1A s1 ECEN 301 Dscusson # Krchhoff s Laws 18
Voltage Mong charges n order to produce a current requres work Voltage: the work (energy) requred to moe a unt charge between two ponts Volt (V): the basc unt of oltage (named after Alessandro Volta) Volt (V): oltage unt. 1 Volt = 1 joule/coulomb (J/C) ECEN 301 Dscusson # Krchhoff s Laws 19
Voltage Voltage s also called potental dfference Very smlar to gratatonal potental energy Voltages are relate oltage at one node s measured relate to the oltage at another node Conenent to set the reference oltage to be zero a ba ab b ab => the work requred to moe a poste charge from termnal a to termnal b ba => the work requred to moe a poste charge from termnal b to termnal a ab = a - b ba = - ab ECEN 301 Dscusson # Krchhoff s Laws 0
Voltage Polarty of oltage drecton (for a gen current drecton) ndcates whether energy s beng absorbed or suppled a ab b a ba b Snce s gong from to energy s beng absorbed by the element (passe element) Snce s gong from to energy s beng suppled by the element (acte element) ECEN 301 Dscusson # Krchhoff s Laws 1
Voltage Polarty of oltage drecton (for a gen current drecton) ndcates whether energy s beng absorbed or suppled a ab b a a ba b Absorbng energy (load) (passe element) POSITIVE oltage 1 1.5 V b ab Supplyng energy (source) (acte element) NEGATIVE oltage ECEN 301 Dscusson # Krchhoff s Laws
Voltage Ground: represents a specfc reference oltage Most often ground s physcally connected to the earth (the ground) Conenent to assgn a oltage of 0V to ground The ground symbol we ll use (earth ground) Another ground symbol (chass ground) ECEN 301 Dscusson # Krchhoff s Laws 4
Krchhoff s Voltage Law (KVL) KVL: energy must be consered the sum of the oltages n a closed crcut must equal zero. N n a n 1 0 1 1.5 V b ab Use Node b as the reference oltage (ground): b = 0 ab 1 ab 0 1 1.5V ab a a ab b 0 1.5 0 1.5V ECEN 301 Dscusson # Krchhoff s Laws 5
Krchhoff s Voltage Law (KVL) Example3: usng KVL, fnd s1 = 1V, 1 = 6V, 3 = 1V 1 V s1 3 Source: loop traels from to termnals Sources hae negate oltage Load: loop traels from to termnals Loads hae poste oltage ECEN 301 Dscusson # Krchhoff s Laws 6
Krchhoff s Voltage Law (KVL) Example3: usng KVL, fnd s1 = 1V, 1 = 6V, 3 = 1V 1 V s1 3 Source: loop traels from to termnals Sources hae negate oltage Load: loop traels from to termnals Loads hae poste oltage ECEN 301 Dscusson # Krchhoff s Laws 7
Krchhoff s Voltage Law (KVL) Example3: usng KVL, fnd s1 = 1V, 1 = 6V, 3 = 1V V s1 1 3 s1 1 3 0 s1 1 5V 6 1 1 3 NB: s the oltage across two elements n parallel branches. The oltage across both elements s the same: ECEN 301 Dscusson # Krchhoff s Laws 8
Krchhoff s Voltage Law (KVL) Example4: usng KVL fnd 1 and 4 s1 = 1V, s = -4V, = V, 3 = 6V, 5 = 1V 1 V s V s1 4 3 5 ECEN 301 Dscusson # Krchhoff s Laws 9
Krchhoff s Voltage Law (KVL) Example4: usng KVL fnd 1 and 4 s1 = 1V, s = -4V, = V, 3 = 6V, 5 = 1V 1 Loop1 Loop V s V s1 4 3 Loop3 5 ECEN 301 Dscusson # Krchhoff s Laws 30
Krchhoff s Voltage Law (KVL) Example4: usng KVL fnd 1 and 4 s1 = 1V, s = -4V, = V, 3 = 6V, 5 = 1V 1 V s1 Loop1 3 Loop 4 Loop3 5 V s s1 1 Loop 1: 3 1 0 s1 1 4V 6 3 ECEN 301 Dscusson # Krchhoff s Laws 31
Krchhoff s Voltage Law (KVL) Example4: usng KVL fnd 1 and 4 s1 = 1V, s = -4V, = V, 3 = 6V, 5 = 1V 1 V s1 Loop1 3 Loop 4 Loop3 5 V s s Loop : 4 4 0 s 4 6V ECEN 301 Dscusson # Krchhoff s Laws 3