Electronics 1: Lecture 2 - Understanding Charge, Voltage, Current, and Kirchhoff's Laws, Study notes of Physics

Download Electronics 1: Lecture 2 - Understanding Charge, Voltage, Current, and Kirchhoff's Laws and more Study notes Physics in PDF only on Docsity! Electronics 1: Lecture 2 • Some Background • Kirchhoff’s Laws • Ohm’s Law • Network Analysis Modified (slightly) from slides originally prepared by Kai Marten’s Electric Charge Fundamental unit in nature: e = 1.60217653(14) 10-19 C http://physics.nist.gov/constants (quarks fractional charges: u,c,t +2/3 d,s,b -1/3) SI fundamental unit Ampere (A): The ampere is that constant current which, if maintained in two straight parallel con- ductors of infinite length, of negligible cir- cular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 10-7 newton per meter of length. http://physics.nist.gov/cuu/Units/ampere.html V Josephson effect Quantum Hall effect Coulomb (C): 1C = 1A 1s No Current, no Action… no threat… … the end Uncontrolled Current, Uncontrolled Action: Your friends: - wrist strap - shielding bag What Makes Charges Move ? Potential difference (i.e. voltage drop) current higher potential: (relative) + where the positive charges go (or the negative come from) lower potential: (relative) - where the negative charges go (or the positive come from) current flows from + to – (source to sink) electrons move from – to + (typically electrons are the nimble carriers of charge that make up currents Electromotive Force (emf) e- e- emf: Moves charges in source to maintain current… Sources: • current sources • voltage sources Modes: • DC (direct current) • AC (alternating current) Symbols: battery V I AC unspecified ideal ?!? Circuit: Designed Pathways for Current Set Light bulb N - Battery Conductor Many Ways (to Obscure) All the same !!! 2 1 3 1 32 Passive Linear Elements: Capacitor with capacitance C: (Q charge; V voltage (drop); I current) Resistor with resistance R: Inductor with inductance L: V = 1 C Q V = R dQ dt = RI V = L d2Q dt 2 = L dI dt Resistor • burns energy • resists current flow and produces voltage drop Symbol: Unit of Resistance: Ohm [ ]: 1 = 1V/1A Most precise component ! Build your circuits so that resistors define the performance! “Other” Types of Capacitors… Inductor • Stores/releases energy in/from magnetic field • resists current changes Symbol: Unit of Inductance: Henry [H]: 1H = 1Vs/1A “Other” Types of Inductors… Network Terminology • Network: an interconnection of (circuit) elements • Circuit: a network with at least one closed path • Branch: a single element in the network • Node: point of connection between two or more branches • Loop: any closed path in a network • Mesh: loop that does not contain any other loop within Elements are in - series if the node between them has no other branches same current - parallel if they are connected to the same two nodes\ same voltage One node will typically be chosen to be the reference or datum node commonly also called ground, abbreviated GND Kirchhoff’s Laws Kirchhoff’s Voltage Law (KVL): Loop Vi = 0 (electric field conservative!) Kirchhoff’s Current Law (KCL): Node Ii = 0 (charge conservation!) Watch your (implicit) sign conventions !!! X Kirchhoff’s Laws again: Kirchhoff’s Voltage Law (KVL): Loop Vi = 0 Kirchhoff’s Current Law (KCL): Node Ii = 0 KVL: All the rest: Ohm’s law: 2 + 4 = 6, 1/3 + 1/6 = , 2 + 9 = 11 (What? !) Nodal Analysis: determine node voltages: Select reference node Apply KCL to each non-reference node Solve the resulting equations… R1 I1 R3 R2 I2 v1v2 GND Let ii be the current through Ri node 1 v1 currents: I1 = I2 + i1 + i2 node 2 v2 currents: I2 + i2 = i3 i2 i1i3 Keep current directions clear by labeling!!! Nodal Analysis (continued) R1 I1 R3 R2 I2 v1v2 GND i1 = (v1-0)/R1 = v1/R1 i2 = (v1-v2)/R2 i3 = (v2-0)/R3 = v2/R3 ii = V/Ri I1 = I2 + i1 + i2 I2 + i2 = i3 I1 = I2 + v1/R1 + (v1-v2)/R2 I2 + (v1-v2)/R2 = v2/R3 2 equations, 2 unknowns solved! I3 Nodal Analysis: Example 2 5A 4 6 1 0 A What do we want to know? V1 V2 Always clearly identify you variables in your circuit diagram !!! V3 = 0 (GND) i1 i2 i3 What are our stepping stones? @v1: i1+i3=5A @v2: @v3: i3+10A=5A+ i2 i1+i2=10A i1=5A - i3 i2=10A - i1 this case: iGND = 0 3 nodes 3 equations; but only 2 independent… + Ohm’s law: v1/2 + (v1-v2)/4 = 5A (v1-v2)/4 + 10A = 5A + v2/6 Solution: v1 = 13.33V, v2 = 20V i3 ?= –1.667A !!! Node or Mesh? non-planar node… else: #nodes < #meshes node #meshes < #nodes mesh also: voltage sources mesh current sources node X X v v1 v2 Superposition 6V 3A 8 4 6V 3A 8 4 6V 3A 8 4 Voltage or current is the sum of all the voltages and currents contributed by each individual voltage and current source: 1. turn off all independent sources save one 2. repeat for all independent sources 3. add the contributions Q: voltage across the 4 resistor: v = v1+v2 1. mesh analysis: (8+4) i1 – 6V = 0 i1 = 0.5A 2. node analysis (ground at bottom!): i2 = 3A (1 – 8 /(4 +8 )) i2 = 2A 3. Sum it: v = 4 i1 + 4 i2 = 2V + 8V = 10V turning off: voltage source short circuit current source open circuit Homework # 1 Due Sept 4 Reading: Bobrow Chapter 1 and 2 2001 lecture notes 1 and 2 Problems: Bobrow 1.17, 1.19, 1.24, 1.30, 1.34 2.1, 2.2, 2.10, 2.19, 2.21