Fundamental Electrical Concepts

Fundamental ElectricalConcepts

Electric Charge (Q) Characteristic of subatomic particles thatdetermines their electromagnetic interactions An electron has a -1.602 10-19 Coulomb charge The rate of flow of charged particles is calledcurrent

Current Current (Number of electrons that pass inone second) (charge/electron) -1 ampere (6.242 1018 e/sec) (-1.602 10-19Coulomb/e) Notice that an ampere Coulomb/second The negative sign indicates that the current inside isactually flowing in the opposite direction of theelectron flowElectronsCurrent

Current i dq/dt – the derivitive or slope of the chargewhen plotted against time in seconds Q i dt – the integral or area under thecurrent when plotted against time in secondsCurrentamps4321Q delivered in 0-5 sec 12.5 Coulombs5 sec

AC and DC Current DC Current has a constant value AC Current has a value that changes sinusoidally Notice that AC currentchanges in value anddirection No net charge istransferred

Why Does Current Flow? A voltage source provides the energy (orwork) required to produce a current Volts joules/Coulomb dW/dQ A source takes charged particles (usuallyelectrons) and raises their potential so theyflow out of one terminal into and through atransducer (light bulb or motor) on their wayback to the source’s other terminal

Terms to Remember The Source can be any source of electrical energy. In practice, there arethree general possibilities: it can be a battery, an electrical generator, orsome sort of electronic power supply. The Load is any device or circuit powered by electricity. It can be as simple asa light bulb or as complex as a modern high-speed computer. (Path) a wire or pathway which will allow electron to flow throughout acircuit. Electricity can be described as the flow of charged particles. If theparticles accumulate on an object, we term this static electricity. (Direct Current) An electrical current that travels in one direction and usedwithin the computer's electronic circuits. (Alternating Current) The common form of electricity from power plant tohome/office. Its direction is reversed 60 times per second. Circuit is a conducting path for electrons.Copyright Texas Education Agency, 2011.All rights reserved.7

Voltage Voltage is a measure of the potential energythat causes a current to flow through atransducer in a circuit Voltage is always measured as a differencewith respect to an arbitrary common pointcalled ground Voltage is also known as electromotive forceor EMF outside engineering

What is Ohm’s Law?Ohm's Law states that, at constant temperature, the electriccurrent flowing in a conducting material is directly proportionalto the applied voltage, and inversely proportional to theResistance.Why is Ohms Law important?Ohm’s Law is the relationship between power, voltage, currentand resistance. These are the very basic electrical units wework with. The principles apply to alternating current (ac),direct current (dc), or radio frequency (rf) .Copyright Texas Education Agency, 2011.All rights reserved.9

Ohm’s LawI V/RGeorg Simon Ohm (1787-1854)I Current (Amperes) (amps)V Voltage (Volts)R Resistance (ohms)

Characteristics of Ohm’s LawVoltage: Difference of potential, electromotive force, ability to dowork.Unit of measure Volt Symbol V (Current: Flow of electrons Unitof measure Ampere Symbol IResistance: Opposition to current flow Unit of measure Ohmoften seen as the Greek letter Omega Symbol RCopyright Texas Education Agency, 2011.All rights reserved.11

A Circuit Current flows from the higher voltage terminal of the sourceinto the higher voltage terminal of the transducer beforereturning to the sourceI TransducerVoltage The source expendsenergy & the transducerconverts it intosomething useful- SourceVoltage-I

circuit diagramScientists usually draw electric circuits using symbols;celllampswitchwires

Simple Circuits Series circuit– All in a row– 1 path for electricity– 1 light goes out and thecircuit is broken Parallel circuit– Many paths for electricity– 1 light goes out and theothers stay on

Series and Parallel Circuits Series Circuits– only one end of each component is connected– e.g. Christmas tree lights Parallel Circuits– both ends of a component are connected– e.g. household lighting

Passive Devices A passive transducer device functions onlywhen energized by a source in a circuit Passive devices can be modeled by a resistance Passive devices always draw current so thatthe highest voltage is present on the terminalwhere the current enters the passive device V 0I 0- Notice that the voltage ismeasured across the device Current is measuredthrough the device

Active Devices Sources expend energy and are consideredactive devices Their current normally flows out of theirhighest voltage terminal Sometimes, when there are multiple sourcesin a circuit, one overpowers another, forcingthe other to behave in a passive manner

Power The rate at which energy is transferred froman active source or used by a passive device P in watts dW/dt joules/second P V I dW/dQ dQ/dt volts amps watts W P dt – so the energy (work in joules) isequal to the area under the power in wattsplotted against time in seconds

Conservation of Power Power is conserved in a circuit - P 0 We associate a positive number for power aspower absorbed or used by a passive device A negative power is associated with an activedevice delivering powerI V-If I 1 ampV 5 voltsThen passiveP 5 watts(absorbed)If I -1 ampV 5 voltsThen activeP -5 watts(delivered)If I -1 ampV -5 voltsThen passiveP 5 watts(absorbed)

Example A battery is 11 volts and as it is charged, itincreases to 12 volts, by a current that startsat 2 amps and slowly drops to 0 amps in 10hours (36000 seconds) The power is found by multiplying the currentand voltage together at each instant in time In this case, the battery (a source) is acting likea passive device (absorbing energy)

Voltage, Current & Power

In this second example, we will calculate the amount of resistance (R) in acircuit, given values of voltage (E) and current (I):What is the amount of resistance (R) offered by the lamp?Copyright Texas Education Agency, 2011.All rights reserved.22

In the last example, we will calculate the amount of voltage supplied by abattery, given values of current (I) and resistance (R):What is the amount of voltage provided by the battery?Copyright Texas Education Agency, 2011.All rights reserved.23

Resistance Property of a device that indicates how freely it willallow current to flow given a specific voltageapplied. If low in value, current flows more freely. Measured in ohms (Ω V/A or KΩ V/mA)R Voltage or V I R This is Ohm’s Law!CurrentI Obeys the passive sign conventionVif I 0 then V 0

Resistors Resistors are devices that are used in a varietyof circuits to make the currents and voltageswhat you desire They are color-coded and come in varioustolerances, 1%, , 5% and , 10% are mostcommon

Resistor Color Code56 * 10 kΩ 560 kΩ237 * 1 Ω 237 Ωhttp://www.elexp.com/t resist.htm

Conductance (G) Conductance is the reciprocal of resistanceIts unit is the siemen amps/volts 1/ΩG I/V 1/RAn equivalent measure of how freely a currentis allowed to flow in a device

Resistivity (ρ) Property of a material that indicates howmuch it will oppose current flow R (ρ · length) / (cross sectional area) Units are ohms · meters (Ω · m) As the wire gets bigger, so does the crosssection making the resistance smaller As the length gets longer, the resistance goesup proportionately

Conductors Materials with electrons that are looselybound to the nucleus and move easily(usually one electron in the outer shell) Their low resistance goes up as thematerial is heated, due to the vibration ofthe atoms interfering with the movementof the electrons The best conductors are superconductors attemperatures near 0o Kelvin

Semiconductors Materials with electrons that are boundmore tightly than conductors (usually 4electrons in the outer shell) Impurities are added in controlled amountsto adjust the resistivity down Semiconductors become better conductorsat higher temperatures because the addedenergy frees up more electrons (eventhough the electron flow is impeded by theincreased atomic vibration)

Insulators Materials that have all 8 electrons in the outershell tightly bound to the nucleus It takes high temperatures or very high electricfields to break the atomic bonds to free upelectrons to conduct a current Very high resistivities and resistances

Resistivity of Materials Glass Gold Silver Silicon Aluminum CopperPut a number 1 besidethe material thatis the best conductor,a 2 next to thematerial next mostconductive, etc.

Resistivity of Materials1 Silver - A conductor - ρ 1.64 ·10-8 ohm-m2 Copper - A conductor - ρ 1.72·10-8 ohm-m3 Gold – A conductor - ρ 2.45·10-8 ohm-m4 Aluminum - A conductor - ρ 2.8·10-8 ohm-m5 Silicon - A semiconductor - ρ 6.4 ·102 ohm-m6 Glass – An insulator – ρ 1012 ohm-m

Example A round wire has a radius of 1 mm 10-3mThe wire is 10 meters longThe wire is made of copperR (1.72 · 10-8 Ω·m · 10 m) /( π ·(10-3m) 2 )R 0.0547 ΩThis is negligible in most circuits whereresistances are often thousands of ohms

Power used by Resistors We saw that P I VIf by Ohm’s law, V I R, then P I2 ROr since I V /R, then P V2 / RSince resistance is always positive for passivedevices, then power is always positive(meaning that power is always absorbed orused)

Kirchoff’s Laws

Circuit Definitions Node – any point where 2 or more circuitelements are connected together– Wires usually have negligible resistance– Each node has one voltage (w.r.t. ground) Branch – a circuit element between twonodes Loop – a collection of branches that form aclosed path returning to the same nodewithout going through any other nodes orbranches twice

Example How many nodes, branches & loops?R1 -VsIsR2R3Vo-

Example Three nodesR1 -VsIsR2R3Vo-

Example 5 BranchesR1 -VsIsR2R3Vo-

Example Three Loops, if starting at node AABR1 -VsIsR2R3Vo-C

Kirchoff’s Voltage Law (KVL) The algebraic sum of voltages aroundeach loop is zero– Beginning with one node, add voltages acrosseach branch in the loop (if you encounter a sign first) and subtract voltages (if youencounter a – sign first) Σ voltage drops - Σ voltage rises 0 Or Σ voltage drops Σ voltage rises

Example Kirchoff’s Voltage Law around 1st LoopAI1 I1R1-BR1I2 -Vs IsR2 I2R2R3Vo-CAssign current variables and directionsUse Ohm’s law to assign voltages and polarities consistent withpassive devices (current enters at the side)

Example Kirchoff’s Voltage Law around 1st LoopAI1 I1R1-BR1I2 -Vs IsR2 I2R2R3Vo-CStarting at node A, add the 1st voltage drop: I1R1

Example Kirchoff’s Voltage Law around 1st LoopAI1 I1R1-BR1I2 -Vs IsR2 I2R2R3Vo-CAdd the voltage drop from B to C through R2: I1R1 I2R2

Example Kirchoff’s Voltage Law around 1st LoopAI1 I1R1-BR1I2 -Vs IsR2 I2R2R3Vo-CSubtract the voltage rise from C to A through Vs: I1R1 I2R2 – Vs 0Notice that the sign of each term matches the polarity encountered 1st

Circuit Analysis When given a circuit with sources andresistors having fixed values, you can useKirchoff’s two laws and Ohm’s law todetermine all branch voltages and currentsVAB - AIB7Ω 3Ω12 v-VBC-C

Circuit Analysis By Ohm’s law: VAB I·7Ω and VBC I·3ΩBy KVL: VAB VBC – 12 v 0Substituting: I·7Ω I·3Ω -12 v 0Solving: I 1.2 A V ABAIB7Ω 3Ω12 v-VBC-C

Circuit Analysis Since VAB I·7Ω and VBC I·3Ω And I 1.2 A So VAB 8.4 v and VBC 3.6 v VAB -AIB7Ω 3Ω12 v-VBC-C

Series Resistors KVL: I·10Ω – 12 v 0, So I 1.2 A From the viewpoint of the source, the 7and 3 ohm resistors in series areequivalent to the 10 ohmsI 12 v-10ΩI·10Ω-

Series Resistors To the rest of the circuit, series resistorscan be replaced by an equivalentresistance equal to the sum of all resistorsSeries resistors (same current through all)II.Σ Rseries