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Transcript
Basic Electrical Engineering Lecture # 02 & 03 Circuit Elements Course Instructor: Engr. Sana Ziafat Agenda • • • • Ideal Basic Circuit Elements Active vs Passive elements Electrical Resistance Kirchhoff’s Laws Circuit Analysis Basics • Fundamental elements ▫ ▫ ▫ ▫ ▫ • • • Voltage Source Current Source Resistor Inductor Capacitor Kirchhoff’s Voltage and Current Laws Resistors in Series Voltage Division Active vs. Passive Elements • Active elements can generate energy ▫ Voltage and current sources ▫ Batteries • Passive elements cannot generate energy ▫ Resistors ▫ Capacitors and Inductors (but CAN store energy) Active and Passive Elements • Active element ▫ a device capable of generating electrical energy Voltage source Current source Power source Batteries Generators ▫ a device that needs to be powered (biased) transistor • Passive element ▫ a device that absorbs electrical energy Resistor Capacitor Inductor motor light bulb heating element Voltage and Current • Voltage is the difference in electric potential between two points. To express this difference, we b a label a voltage with a “+” and “-” : 1.5V Here, V1 is the potential at “a” minus + V1 the potential at “b”, which is -1.5 V. • Current is the flow of positive charge. Current has a value and a direction, expressed by an arrow: i1 Here, i1 is the current that flows right; i1 is negative if current actually flows left. • These are ways to place a frame of reference in your analysis. Electrical Source • Is a one that converts electrical energy to non electrical or vice versa. For example; 1. Discharging battery 2. Charging battery 3. Motor 4. Generator Ideal Voltage Source • The ideal voltage source explicitly defines the voltage between its terminals. Vs ▫ Constant (DC) voltage source: Vs = 5 V ▫ Time-Varying voltage source: Vs = 10 sin(t) V ▫ Examples: batteries, wall outlet, function generator, … • The ideal voltage source does not provide any information about the current flowing through it. • The current through the voltage source is defined by the rest of the circuit to which the source is attached. Current cannot be determined by the value of the voltage. • Do not assume that the current is zero! Ideal Current Source • The ideal current source sets the value of the current running through it. Is ▫ Constant (DC) current source: Is = 2 A ▫ Time-Varying current source: Is = -3 sin(t) A • The ideal current source has known current, but unknown voltage. • The voltage across the current source is defined by the rest of the circuit to which the source is attached. • Voltage cannot be determined by the value of the current. • Do not assume that the voltage is zero! “IDEAL” or “Independent” Sources • IDEAL voltage source • IDEAL current source ▫ maintains the prescribed voltage across its terminals regardless of the current drawn from it ▫ maintains the prescribed current through its terminals regardless of the voltage across those terminals LOADCurrent + 0.012 A LOAD Is 1A + - LOADVoltage 999.001 V DC 1MOhm Z=A+jB Vs 12 V Z=A+jB DC 1e-009Ohm LOAD “Controlled” or “Dependent” Sources • A voltage or current source whose value “depends” on the value of voltage or current elsewhere in the circuit • Use a diamond-shaped symbol ECE 201 Circuit Theory I 11 Voltage-Controlled Current Source VCCS + Vx - Is 1 Mho Is = aVx • Is is the “output” current • Vx is the “reference” voltage • a is the multiplier • Is = aIx Current-Controlled Current Source CCCS Ix Is 1 A/A Is=bIx • Is is the “output” current • Ix is the “reference” current • b is the multiplier • Is = bIx Resistors • A resistor is a circuit element that dissipates electrical energy (usually as heat) • Real-world devices that are modeled by resistors: incandescent light bulbs, heating elements (stoves, heaters, etc.), long wires • Resistance is measured in Ohms (Ω) Resistor • The resistor has a currentvoltage relationship called Ohm’s law: v=iR where R is the resistance in Ω, i is the current in A, and v is the voltage in V, with reference directions as pictured. i + R v • If R is given, once you know i, it is easy to find v and vice-versa. • Since R is never negative, a resistor always absorbs power… Ohm’s Law v(t) = i(t) R - or p(t) = i2(t) R = v2(t)/R V=IR [+ (absorbing)] i(t) The Rest of the Circuit +v(t) R – Open Circuit • What if R = ? i(t)=0 + The Rest of the Circuit v(t) – i(t)=0 • i(t) = v(t)/R = 0 Short Circuit • What if R = 0 ? • v(t) = R i(t) = 0 i(t) The Rest of the Circuit + v(t)=0 – Basic Circuit Elements • Resistor ▫ Current is proportional to voltage (linear) • Ideal Voltage Source ▫ Voltage is a given quantity, current is unknown • Wire (Short Circuit) ▫ Voltage is zero, current is unknown • Ideal Current Source ▫ Current is a given quantity, voltage is unknown • Air (Open Circuit) ▫ Current is zero, voltage is unknown • Reciprocal of resistance is conductance • Having units of Simens • G= 1/R Simens (s) • Power calculations at terminals of Resistor???? Wire (Short Circuit) • Wire has a very small resistance. • For simplicity, we will idealize wire in the following way: the potential at all points on a piece of wire is the same, regardless of the current going through it. ▫ Wire is a 0 V voltage source ▫ Wire is a 0 Ω resistor Air (Open Circuit) • Many of us at one time, after walking on a carpet in winter, have touched a piece of metal and seen a blue arc of light. • That arc is current going through the air. So is a bolt of lightning during a thunderstorm. • However, these events are unusual. Air is usually a good insulator and does not allow current to flow. • For simplicity, we will idealize air in the following way: current never flows through air (or a hole in a circuit), regardless of the potential difference (voltage) present. ▫ Air is a 0 A current source ▫ Air is a very very big (infinite) resistor • There can be nonzero voltage over air or a hole in a circuit! Kirchhoff’s Laws • The I-V relationship for a device tells us how current and voltage are related within that device. • Kirchhoff’s laws tell us how voltages relate to other voltages in a circuit, and how currents relate to other currents in a circuit. Kirchhoff’s Laws • Kirchhoff’s Current Law (KCL) ▫ Algebraic sum of current a any node in a circuit is zero • Kirchhoff’s Voltage Law (KVL) ▫ sum of voltages around any loop in a circuit is zero KCL (Kirchhoff’s Current Law) i1(t) i5(t) i2(t) i4(t) i3(t) The sum of currents entering the node is zero: n i (t ) 0 j 1 j Analogy: mass flow at pipe junction Kirchhoff’s Voltage Law (KVL) a b • Suppose I add up the potential drops + Vab around the closed path, from “a” to “b” to “c” and back to “a”. + • Since I end where I began, the total Vbc drop in potential I encounter along the path must be zero: Vab + Vbc + Vca = 0 c • It would not make sense to say, for example, “b” is 1 V lower than “a”, “c” is 2 V lower than “b”, and “a” is 3 V lower than “c”. I would then be saying that “a” is 6 V lower than “a”, which is nonsense! • We can use potential rises throughout instead of potential drops; this is an alternative statement of KVL. Writing KVL Equations 1 + va b What does KVL say about the voltages along these 3 paths? + v2 + vb - 3 Path 1: va v 2 vb 0 Path 2: vb v 3 vc 0 Path 3: va v2 v3 vc 0 v3 2 + a c + vc Kirchhoff’s Current Law (KCL) • Electrons don’t just disappear or get trapped (in our analysis). • Therefore, the sum of all current entering a closed surface or point must equal zero—whatever goes in must come out. • Remember that current leaving a closed surface can be interpreted as a negative current entering: i1 is the same statement as -i1 KCL Equations In order to satisfy KCL, what is the value of i? KCL says: 24 μA + -10 μA + (-)-4 μA + -i =0 24 mA -4 mA 18 μA – i = 0 i = 18 μA 10 mA i Readings • Chapter 2: 2.1, 2.2, 2.4 (Electric Circuits) ▫ By James W. Nilson Q&A