# MEP 382: Design of Applied Measurement Systems Lecture 3: DC & AC Circuit Analysis

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1 Faculty of Engineering MEP 38: Design of Applied Measurement Systems Lecture 3: DC & AC Circuit Analysis

2 Outline oltage and Current Ohm s Law Kirchoff s laws esistors Series and Parallel oltage Dividers Capacitors, Inductors and -C circuits

3 Basic Electrical Circuit Higher electrical Potential Light Heat oltage Source Lower Electrical Potential oltage difference in potential energy, Current flows from regions of higher electrical potential to regions of lower electrical potential. Electrical Energy only flows in a closed path closed system DC (Direct Current) are those circuits with static or slowly varying values. AC (Alternating Current) signals are those with rapid change or regular periodic change source of these terms is a historical artifact Wires are considered ideal no resistance to flow of electrical energy The filament wire in the light bulb is a resistor that converts energy to light and heat

4 Simple Analogy oltage is a measure of electrical potential energy (units are volts) You can think of it as potential energy like water in a reservoir at the top of a hill The lowest energy state in the circuit is called Ground standing water at the bottom of the hill Current is the flow of electrons from a high energy state to a lower energy state (units are amperes) You can think of it as water flowing through pipes from the top to the bottom of a hill esistance is like narrow parts of the pipe (units are ohms) The more constrictions that are put in series, the slower the flow rate Total flow capacity is divided among parallel paths but the water has the same energy at the top and bottom of each parallel path Capacitance is like a little tank along the way (units are farads) Water (and potential energy in the form of a charge) can accumulate in the tank Just as the water s potential energy is converted to kinetic energy (velocity) as it moves down the hill, so is electrical energy converted into other forms of energy along the way (heat, light, mechanical energy) If you take this analogy too far, it breaks down, but it is a good place to start

5 Water Analogy Tank at the top of the hill esistors are like pipes A voltage source Is like a pump moving water from low potential energy (low altitude) to higher potential energy (higher altitude) Capacitors are like little tanks along the way Tank at the Bottom of the Hill (Ground)

6 Current Definitions Current is defined as flowing from higher potential energy to lower potential energy This is often expressed as flow from to This convention existed before the discovery of the electron, the basic atomic unit that carries electrical energy Electrons are negatively charged, so they actually flow from to, the opposite of current In almost all applications, we use the concept of current as our model/reference system Current is almost always represented by the variable I (i)

7 oltage Sources Series and Parallel In series, voltage sources add to increase voltage with no increase in current capacity Actual current may rise as voltage rises with a fixed resistive load In parallel, voltage sources do not increase voltage but they do increase the current capacity Exactly predicting the voltages requires a current loop analysis volts olts

8 Kirchoff slaws oltage The sum of voltage drops and rises around any path in a circuit in a closed path (start and end at the same point) must equal zero Since the voltage at any point in a circuit is an electrical energy potential, any path around the circuit must end up at the same energy potential or else the law of conservation of energy would be violated Current The sum of all the current entering a node of a circuit and leaving the node of a circuit must equal zero Since current is just the flow of electrons and electrons have an energy state and mass this is just a restatement of the laws of conservation of energy and conservation of mass i in I i in i3 out i i

9

10 Ohm s Law oltage Current x esistance voltage, I current, resistance I, I /, /I if you know can calculate the third Almost every measuring circuit in this course will use this relationship Symbol for resistor.5 olts AA Battery.5 olts - 0 olts KiloOhm resistor Also called the Load Ω Current I.5 olts/000 Ohms.005 amperes.5 milliamps

11 Short Circuits and Open Circuits A short circuit is when the and of a voltage source are directly connected with zero or essentially zero resistance A wire or a piece of metal can do this Due to Ohm s law, when is zero or near zero then current goes to infinity (/I) This results in rapid heating and overloading the voltage supply An open circuit is when the and of a voltage source are not connected or connected by a very high resistance (> 00 Megaohms) In this case no current flows

12 oltage Sources In Series and Parallel I tot tot Load I Load I tot Load I tot I ( I I I ) max Load Load.5 I.5 I max For parallel sources, max is the highest of the two voltages. Exactly predicting the voltages requires a current loop analysis Load Itot

13 Property of material

14 esistors Series esistors in series add This type of circuit is a voltage divider if resistors are equal the intermediate voltage will be half 3 tot I ) ( ) ( ) ( I I I I tot tot

15 esistors - Parallel esistors in parallel add inverse This type of circuit is a current divider if resistances are equal, current down one leg is half of the current of a single resistor I I tot tot tot n I I tot... n Itot I I tot

16 oltage divider as the basis for instrumentation Circuits For all resistive sensors, the voltage divider is the primary circuit used in instrumentation esistive sensors are those whose resistance value changes with change in the measured quantity e.g. esistance Temperature Detector (TD) resistance changes with temperature, Strain Gage resistance changes with strain) sensor known sensor sensor Temperature known ( ) Known oltage () Known esistor (known) esistive Sensor (sensor) oltage Measurement Proportional To Sensor alue ()

17 Sensors for Current Two types of sensors are used for current- Ammeters A shunt which is a precision very low resistance resistor over which a voltage drop is observed Typically large blocks of metal to dissipate heat Must cause minimum additional voltage drop typically millivolts A clamp An inductive sensor which surrounds a wire converting the electromagnetic field into a small AC current that can be read by a smaller meter with a shunt Current through only one conductor is measured If put both in the meter, they cancel out

18 Use of Digital Multi Meter (DMM) DMM Using DMM as ammeter Load - - DMM Using DMM as voltmeter or ohmmeter To measure voltage (voltmeter function), measure ACOSS the load In parallel with the load To measure current (ammeter function), you have to measure through the load In series with the load To measure resistance (ohmmeter function), the circuit must be unpowered and then measure across the load You may have to remove the component to get an accurate reading as there may be other paths through the circuit that the ohmmeter function will measure

19 esistor Color Code Color st and nd Band 3rd Band Black 0 x Brown x0 ed x00 Orange 3 x000 Yellow 4 x0,000 Green 5 x00,000 Blue 6 x,000,000 iolet 7 x0,000,000 Gray 8 x00,000,000 White 9 x,000,000,000

20

21 DC Power Power oltage x Current I Since I (Ohms Law), Power also I^ for purely resistive direct current circuits Direct current (DC) where there is no periodic change in voltage or current Alternating current (AC) where there is periodic change in frequency and current Power is in watts A 9 battery with a 000 ohm resistor ( kilo-ohm) across the terminals will have.009 amps running through it which will generate.08 watts A 9 battery with a 0 ohm resistor across it will have.9 amps which will generate 8. watts

22 Capacitors and Inductors Capacitors store electrical energy in static charge Current is a function of the change in voltage with respect to time Often made by a dielectric between two parallel plates Inductors store electrical energy in an electromagnetic field oltage is a function of the change in current Often implemented by a coil of wire Symbol for capacitor Symbol for inductor

23 Introduction To Capacitors Capacitance of a device made from two parallel plates separated by a dielectric is C The dielectric constant times the area of the plate divided by the distance between the plates Capacitance is larger as the area of the plates increases and is smaller as the distance between the plates increases Capacitance measured in FAADS which are very large units of measure. Most electronic circuits uses capacitances in the micro-farad to picofarad range Most batteries are just special capacitors Energy stored in a capacitor One half of the capacitance times the voltage squared E ε A D Symbol for capacitor C

24 Capacitors Can act as integrators and ac filters C Can act as differentiators and DC blocks C

25

26 Alternate Symbol for capacitor

27

28 C Circuit Is like filling a closed tank, current keeps flowing until the tank is full, and then it stops flowing Labview I simulates and predicts this AA Battery.5 olts KiloOhm resistor Ω microfarad capacitor

29

30 Charge-Discharge of a microfarad capacitor with a MegaOhm resistor Discharge initiated at t000 msec

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