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 label a voltage with a “+” and “-” : Here, V 1 is the potential at “a” minus 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: Here, i 1 is the current that flows right; i 1 is negative if current actually flows left. These are ways to place a frame of reference in your analysis. 1.5V a b V1V1 - + i1i1

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. ▫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!   VsVs

Ideal Current Source The ideal current source sets the value of the current running through it. ▫Constant (DC) current source: I s = 2 A ▫Time-Varying current source: I s = -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! IsIs

“IDEAL” or “Independent” Sources IDEAL voltage source ▫maintains the prescribed voltage across its terminals regardless of the current drawn from it IDEAL current source ▫maintains the prescribed current through its terminals regardless of the voltage across those terminals

ECE 201 Circuit Theory I 11 “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

Voltage-Controlled Current Source VCCS I s is the “output” current V x is the “reference” voltage a is the multiplier I s = aIx

Current-Controlled Current Source CCCS I s is the “output” current I x is the “reference” current b is the multiplier I s = 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 current- voltage relationship called Ohm’s law: v = i R 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. 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…  + v R i

Ohm’s Law v(t) = i(t) R- or -V = I R p(t) = i 2 (t) R = v 2 (t)/R [+ (absorbing)] v(t)v(t) The Rest of the Circuit R i(t)i(t) + –

Open Circuit What if R =  ? i(t) = v(t)/R = 0 v(t)v(t) The Rest of the Circuit i(t)=0 + –

Short Circuit What if R = 0 ? v(t) = R i(t) = 0 The Rest of the Circuit v(t)=0 i(t)i(t) + –

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) The sum of currents entering the node is zero: Analogy: mass flow at pipe junction i1(t)i1(t) i2(t)i2(t)i4(t)i4(t) i5(t)i5(t) i3(t)i3(t)

Kirchhoff’s Voltage Law (KVL) Suppose I add up the potential drops around the closed path, from “a” to “b” to “c” and back to “a”. Since I end where I began, the total drop in potential I encounter along the path must be zero: V ab + V bc + V ca = 0 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. a b c + V ab - + V bc - V ca +

Writing KVL Equations What does KVL say about the voltages along these 3 paths? Path 1: Path 2: Path 3: vcvc vava ++ ++  vbvb v3v3 v2v2 + - a b c

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: i1i1 is the same statement as -i 1

KCL Equations In order to satisfy KCL, what is the value of i? KCL says: 24 μA μA + (-)-4 μA + -i =0 18 μA – i = 0 i = 18 μA i 10  A 24  A -4  A

Readings Chapter 2: 2.1, 2.2, 2.4 (Electric Circuits) ▫By James W. Nilson

Q & A