ECE 3336 Introduction to Circuits & Electronics

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Note Set #1Voltage, Current, Energy and Power

Spring 2015,TUE&TH 5:30-7:00 pmDr. Wanda Wosik

Introduction to EE

• Basic concepts in circuits: – Current– Voltage– Polarities (reference and actual)

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Analogy to Hydraulic Systems

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Charge

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proton: + charge

electron: - charge

1 proton: q = 1[C]/ 6.2414 x1018 = 1.6022 x10 -19 [C]

1 electron: q = -1.6022 x 10 -19 [C]

Atomic number of atom = # protons or electrons / atom

Here the atom is negatively charged

1.0 eV = 1.60221x10-19 C * 1.0 V=1.60221x10-19 J

The energy acquired by an electron when accelerated by 1.0 V is 1.0 eV.

1C=Q(6.2414 x1018) electrons

ExampleExample

How many Cu atoms have -1 [How many Cu atoms have -1 [CC] of electrons?] of electrons?

Atomic number = 291 atom: qe = 29 (-1.6022 x10-19 ) [C]

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1[C]atoms

29 1 6022 10 [C/atom]#

.

so

17# atoms 2 1522 10. or

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Current

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Current is the rate of flow of charge

water analogy:

pipe with water

wire with current

+ + + + current flows from left to right

Convention: current flows in the direction of positive charge motion (established by Benjamin Franklin).

Hydraulic analogyWater flow in the pipe

Current

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In reality, the electrons are the charges that move in a wire.

Convention: electrons moving in one direction is equivalent to positive charges moving in the other direction.

Ions do not move

+ + + +

• [Ampere] = 1 [Coulomb] of charge moving per [second]

1[A] = 1[Coul/sec]

• The number of charges per second flowing for each Ampere of current is called a Coulomb, which is about 6.24 x 1018 electron charges.

+ Charges flowing is equivalent to - Charges flowing in the opposite direction

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Current [unit]

+ + + +1 [A]

flow rate = 1 [C/s]

1C/1.6022 x10 -19[C]

Current: Formal Definition• Current is the net flow of charges, per time, past an arbitrary “plane” in

an electrical device (the simplest will be a resistor).

• We will only be concerned with the flow of positive charges. • A negative charge moving to the right is conceptually the same as a

positive charge moving to the left. • In conductors electrons=negative charges flow and constitute current.

• Mathematically, current is expressed as…

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Current,typically in

Amperes [A]

Charge, typically in Coulombs [C]

Time, typically in seconds [s]

Current (cont.)

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In fact + charges can also flow ≈ current flows

In semiconductors, both electrons (-) and holes (+) are the charges that move: diodes, transistors, some resistors.

In electrochemistry + ions flow ionic current: metal electroplating, fluidics, plasma etc.

www.saskschools.ca/curr_content/chem30_05/6_redox/redox2_2.htm

Definition of Current

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Current I is a flow of charge. • If the flow is constant, charge does not change q/t and it lasts some time (t), we can find relation

• In the case of “alternating current” ac, there is instantaneous charge change and we have

All electrons (it is a conductor) flow - + with drift velocity v

dN – total # of charges passing the area A carrier density n – this varies with materials

- +

Area

Change of charge in unit time

Hydraulic Analogy for Current• More intuitive analogy: current flow is analogous to the water flow.

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Animated graphic provided by David Warne, student in UH ECE Dept.

Illustration: Water flow and Current

• Water flow rate is determined by the volume of water moving (measured at inserted plane) in a second

• Current is the number of positive charges moving in a second (measured also at such plane).

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Animated graphic provided by David Warne, student in UH ECE Dept.

Voltage

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Potential energy describes the capacity to do work ex. E=mgh (gravitation) will change to kinetic energy E=mv2/2.

q

Electric potential energy U: refers to a charge q moved in an electric field E generated by another charge Q. Charge will experience force F.

Voltage=Work done per unit charge

Voltage ~ to energy (U) loss/gain

Ex. q=1C, VAB=1VEnergy gain/loss 1Joulek=1/4π0

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

Voltage Equipotential lines

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elewor.html

From Coulomb Law:

Voltage: Formal Definition• When we move a charge in the presence of other

charges, energy is transferred. • Voltage corresponds to the change in potential energy

as we move between two points; it is a potential difference.

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Voltage,typically in

Volts [V]

Energy, typically in Joules [J] (or in eV)

Charge, typically in Coulombs [C] (or expressed as e)

Voltage [unit]

• Unit: Volt. • Volt is defined as Joule per Coulomb

• Verify units: V=J/C

• Remember that voltage is defined in terms of the energy gained or lost by the movement of positive charges.

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ex. 1V=1J/1C

Hydraulic Analogy With Two Paths

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Water is flowing through the pipes (analogy to current).

The height difference for water•Pressure

Potential difference•Voltage

Hydraulic Analogy:Voltage and Current

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height ~ voltageflow rate ~ current

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Hydraulic Analogy:Voltage and Current

Nigel P. CookElectronics: A Complete Course, 2e

Copyright ©2004 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458

All rights reserved.21

Physical Appearance. Schematic Symbol.

The BatteryA Source of Voltage.

Using the Voltmeter to Measure Voltage.

Nigel P. CookElectronics: A Complete Course, 2e

Copyright ©2004 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458

All rights reserved.

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Polarities

Polarity refers to • Directions of currents• Signs of voltages

It is extremely important to know the polarity of the voltages and currents in circuits.

Use:• Reference polarities i.e. assumed (chosen) direction for the

purposes of keeping track• Actual polarities i.e. real current and voltage directions

calculated from a circuit.

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Polarities for Currents• For current, the reference polarity is given by an arrow. • The actual polarity is indicated by a value that is associated with

that arrow.

• In the diagram below, the currents i1 and i2 are not defined until the arrows are shown.

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Polarities for Voltages• For voltage, the reference polarity is given by a + symbol and a –

symbol, at or near the two points involved.

• The actual polarity is indicated by a value that is placed between the +

and - symbols.

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• Basic concepts: energy and power• Sign Conventions for power direction

– Energy /power can be delivered or absorbed

• Hydraulic analogy to energy and power helps to visualize electricity

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Energy and Power

Energy• It is the ability to do work.• Energy can have many forms: heat, light,

sound, motion etc.

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Unit is Joule or [J] 1 [Joule]=[Newton•meter].

In everything that we do in circuit analysis, energy will be conserved.

Circuit elements can absorb or deliver energy.

Power• Power is the rate of change of the energy, with time. It is the rate

at which the energy is absorbed or delivered.

• Power can be absorbed or delivered.

• Units: Watts or [W]. Defined as a [Joule per second] W=J/s

• Light bulbs are rated in [W]. Thus, a 100 [W] light bulb is one that absorbs 100 [J] every second that it is turned on.

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Power,typically inWatts [W]

Energy, typically in Joules [J]

Time, typically in seconds [s]

Power from Voltage and Current

• Power can be found from the voltage and current.

• Note that if voltage is given in [V], and current in [A], power will come out in [W].

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Verify units: W=J/s=J/C•C/s=V•A

Sign Conventions or Polarity Conventions

• Sign conventions, or polarity conventions determine whether power and energy are delivered or absorbed

• A sign convention is a relationship between reference polarities for voltage and current.

• As in all reference polarity issues, you can’t choose reference polarities wrong.

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Passive Sign Convention – Definition

• The passive sign convention is when the reference polarity for the current is in the direction of the reference voltage drop

• i.e. current enters the positive terminal for the reference polarity for the voltage.

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Passive Sign Convention (examples)

• The circuits shown have reference polarities which are in the passive sign convention.

• They look different, but the circuits have the same

relationship between the polarities of the voltage and current.

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Active Sign Convention

• The active sign convention is when the reference polarity for the current is in the direction of the reference voltage rise.

• Same as current entering the negative terminal for the reference polarity for the voltage.

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Using Sign Conventions for Power Direction

• The sign conventions will be used to determine whether power is absorbed, or power is delivered.

• We might want to write an expression for power absorbed by a device, circuit element, or other part of a circuit. Use appropriate subscripts.

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Using Sign Conventions for Power Direction

The sign conventions are used to determine whether power is absorbed or delivered.

• In passive sign convention: • (+) vi indicates the power absorbed• (-) vi indicates the power delivered.

• In active sign convention: • (+) vi indicates the power delivered• (–) vi indicates the power absorbed.

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  Passive Convention

Active Convention

Power absorbed

pABS = vi pABS = -vi

Power delivered

pDEL = -vi pDEL = vi

Power Direction TableChoice of •Passive Convention (+ power for passive elements= power absorbed)•Active Convention (+ power for active elements=power delivered)

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  Passive Convention

Active Convention

Power absorbed

pABS = vi pABS = -vi

Power delivered

pDEL = -vi pDEL = vi

Active sign convention.

Passive sign convention.

is

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Figure 2.22, 2.24

The passive sign convention used here (a and b)

Power (p=v • i):pabs,B=-12 V•0.1 A=-1.2 Wpabs,1=8 V•0.1 A=0.8 Wpabs,2=4 V•0.1 A=0.4 W

The battery generates 1.2 WResistors absorb (0.8+0.4) WSo the energy is conserved

Power (p=v • i):pabs,B=-(-12 V)•(-0.1 A)=-1.2 Wpabs,1=-8 V•-0.1 A=0.8 Wpabs,2=-4 V•-0.1 A=0.4 WWe have the same results:The battery generates 1.2 WResistors absorb (0.8+0.4) WSo the energy is conserved

Passive sign gives + power

Passive sign gives - power

dissipated=absorbedgenerated=delivered

Generates energy

Dissipates energy

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In a typical lightning strike, 500 megajoules of electric potential energy are converted into 500 megajoules (total) of light energy, sound energy, thermal energy, and so on.

Energy Conservation andConversion of Energy Chemical,

Thermal, Electrical, Mechanical,Optical etc.

wikipedia.org

Energy and Power in Electrical Systems

• Power delivered to the electrical system comes from other sources (ex. other electrical systems, light sources, thermoelectric materials, chemical battery etc.)

• Since energy is conserved the power will be conserved as well.

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Energy and Power in Electrical Systems

• Power from the electrical system is absorbed by the “energy converter” and results in delivery of new energy forms ex. mechanical (electrostriction), light (LED, lasers), heat, chemical etc.

• Again, since energy is conserved the power will be conserved as well.

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DC Circuit Water Analogy

41http://hyperphysics.phy-astr.gsu.edu/hbase/electric/watcir.html

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DC Circuit Water Analogy

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/watcir.html

Main Points• Current[A]=flow of + charges (or - in the opposite direction)

• Votage[V]=potential difference (=Efield/xdistance)

• Power[W]=vi • conventions: passive and active define delivered and

absorbed power

• Power (and energy is conserved)

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