Ohm’s Law, Power, and Energy

8/13/2019 Ohm’s Law, Power, and Energy

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Ohm€s Law, Power, and Energy

A. Nerves

OBJECTIVES

€ Understand the importance of Ohm•s law and howto apply it to a variety of situations.

€ Be able to plot Ohm•s law and understand how to‚readƒ a graphical plot of voltage versus current.

€ Become aware of the differences between powerand energy levels and how to solve for each.

€ Understand the power and energy flow of asystem, including how the flow affects theefficiency of operation.

€ Become aware of the operation of a variety offuses and circuit breakers and where each isemployed.

OHM€S LAW

€ The first equation to be described iswithout question one of the most importantto be learned in this field.

€ It is applicable to dc circuits, ac circuits,

digital and microwave circuits, and, in fact,any type of applied signal.

€ In addition, it can be applied over a periodof time or for instantaneous responses.

€ The equation can be derived directly from

the following basic equation for all physicalsystems:

OHM€S LAW

€ Every conversion of energyfrom one form to anothercan be related to thisequation.

€ In electric circuits, theeffect we are trying to

establish is the flow ofcharge, or current.

€ The potential difference, orvoltage, between twopoints is the cause(‚pressureƒ), and the

opposition is the resistanceencountered.

OHM€S LAW

€ Georg Simon Ohm, a German physicist,

identified several cause-and-effect

relationships between circuit current,

voltage, and resistance.

€ Ohm stated that current is directly

proportional to voltage and inversely

proportional to resistance.

OHM€S LAW

€ Ohm•s law can be statedmathematically as

I = the circuit current

E = the applied voltage

R = the circuit resistance

OHM€S LAW

Two statements we can derive from Ohm•s law are:

1. The current through a fixed resistance:

a. increases when the applied voltage increases.b. decreases when the applied voltage

decreases.

2. The current generated by a fixed voltage:a. decreases when the resistance increases.

b. increases when the resistance decreases. 8

OHM€S LAW

FIG. 4.2 Basic circuit.

OHM€S LAW

FIG. 4.3 Defining polarities.

OHM€S LAW

FIG. 4.4 Example 4.3.

The Relationship Between

Current and Voltage

•If voltage increases, current will increase if

resistance remains constant.

•The greater the voltage, the higher the current

for any fixed resistance.

Using Ohm€s Law to Calculate

Current

€ Ohm•s law can be used to calculate current in

this circuit as

‚€€

Current

€ The DC power supply has a maximum output of 200 V.

Will the fuse blow?

€ We solve for current as AV

E I 06.6

200€

‚€€

€ The fuse will blow.16

Voltage

€ Ohm•s law can be used to calculate voltage in

this circuit as

V mA R I E 15100150 €‚ƒ€ƒ€

Voltage

€ Two 6 „ speakers draw 2.08 A each from a DC

power supply. Solve for the source voltage.

€ The source voltage is found as

V A R I E 5.12608.2 €‚ƒ€ƒ€

Resistance

€ Ohm•s law can be used to calculate voltage in

this circuit as‚€€€ 200

Resistance

€ Solve for the minimum allowable rheostat

setting that will not cause the fuse to blow.

… The minimum resistance is found as

‚€€€ 602

120(min)

Current & Voltage

€ Current is directly proportional to voltage. … If voltage triples:

E I 18

360€

‚€€

Current triples if voltage triples.It is directly proportional to voltage.

Current & Resistance

€ Current is inversely proportional to resistance.€ If resistance triples

240€

‚€€

Tripling the resistance caused current to drop

to 1/3 of its original value.22

Ohm€s Law Wheel

€ Cover the value of interest to see the correct

equation.

Troubleshooting with Ohm€s

€ Troubleshooting is the process of locating

circuit faults.

€ If a circuit is not operating as it should,Ohm•s law can help find the problem.

€ The first step is to determine the type of

circuit failure.

Troubleshooting with Ohm€s Law:

Current Too Low

€ Ohm•s law tells us that there are tworeasons why current may be too low.

€ The applied voltage is too low.

… Current is directly proportional to voltage. … If the applied voltage is too low then circuitcurrent will be too low.

€ The circuit resistance is too high.

… Current is inversely proportional to resistance.

… If circuit resistance is too high, circuit currentwill be too low.

Troubleshooting with Ohm€s Law:

Current Too High

€ Ohm•s law tells us that there are tworeasons why current may be too high.

€ The applied voltage is too high.

… Current is directly proportional to voltage.

… If the applied voltage is too high then circuitcurrent will be too high.

€ The circuit resistance is too low.

… Current is inversely proportional to resistance.

… If circuit resistance is too low, circuit currentwill be too high.

Summary of Ohm€s Law

Relationships

€ This table summarizes the Ohm•s law

relationships between voltage, current and

resistance.

PLOTTING OHM€S LAW

€ Graphs, characteristics, plots, and the like

play an important role in every technical

field as modes through which the broad

picture of the behavior or response of a

system can be conveniently displayed.

€ It is therefore critical to develop the skills

necessary both to read data and to plot

them in such a manner that they can be

interpreted easily.

FIG. 4.6 Plotting Ohm€s law.

FIG. 4.7 Demonstrating on an I-V

plot that the lower the resistance, the

steeper is the slope.

FIG. 4.8 Applying Eq.

(4.7).

FIG. 4.10 Semiconductor diode

characteristics.

€ In general, the term power is applied

to provide an indication of how much

work (energy conversion) can be

accomplished in a specified amountof time; that is, power is a rate of

doing work.

€ Since energy is measured in joules (J) andtime in seconds (s), power is measured in

joules/second (J/s).

€ The electrical unit of measurement for

power is the watt (W), defined by:

€ In equation form, power is determined by:

FIG. 4.12 Defining the power to a resistive

element.

€ The power associated with any

supply is not simply a function of the

supply voltage. It is determined by the

product of the supply voltage and itsmaximum current rating.

Calculating Power

€ The ampere is defined as

€1 A = 1 coulomb per second

€ The volt is defined as

€1 V = 1 joule per coulomb

€ If we multiply amperes times volts, the results is

in joules per second, the unit of measure for

power.

ond jouleCoulomb Joule

ond Coulomb sec/1

sec11 €ƒ

Watt€s Law

€ One form of Watt•s law can be stated as

€For the circuit shown,

.EIP ƒ€

kW AV E I P 2.210220 €ƒ€ƒ€

Watt€s Law

€ Another form of Watt•s law is P = IƒE = IƒIR or

€ P = I2R

W mA R I P 125500)500(

22€‚ƒ€ƒ€

Watt€s Law

€ The third form of Watt•s law is P = IƒE = (E/R)ƒE or

€ P = E2/R

W V R E P 144

100120

€‚

€€

FIG. 4.14 The nonlinear I-V characteristics of a 75 W lightbulb (Example 4.8).

Power & Heat

€ Energy can not be created or destroyed .

€ It can only be converted into another form.

… A toaster converts electrical energy into heat. … A light bulb converts electrical energy into

light.

… A motor converts electrical energy into

mechanical energy (movement).€ A device that converts energy from one

form to another is called a transducer . 45

Power Conversion

€ Power, like energy, can be converted from

one form to another.

… A DC power supply converts AC power to DC

power and then the DC load may convert theDC power into another form.

Resistor Power Ratings

€ Resistors dissipate power as heat.

… The larger the resistor, the more heat it can

dissipate.

… Standard resistor power ratings are

1 W, † W,

‡ W, and

1/8 W.

Basic Circuit Calculations

€ There are six basic forms and Ohm•s Law and

Watt•s Law:

R I E ƒ€

. E I P ƒ€ R I ƒ€

Finding the Right Equation

€ In some cases none of the six basic equations

can be used to solve a circuit analysis problem.

… When this is the case, you may have to rearrange one

of the basic equations.

… For example, if voltage and power are known, and youwish to solve for resistance, find an equation with all

the variables, and then rearrange it to solve for the

unknown value.

.22 E Rtotransposed is E P €€

The Simplest Circuit

€ The simplest electrical circuit contains a source,

a load, and the necessary conductors to connect

them together.

… The source supplies the power to the load.

… The load dissipates the power as heat, light,

mechanical energy, or some other form.

Sources and Loads

€ A source can be as simple as a battery, or

very complex.

… A surround-sound receiver could be

considered a source for the system speakers.€ A load can also be simple or complex.

… A laptop computer could be considered a load

for its battery.

€ Whenever a load draws the maximumcurrent from its source, this is considered

to be a full load . 51

Circuit Faults: The Open Circuit

€ An open circuit is a physical break in the

conduction path.

… Circuit resistance is close to infinite.

… Circuit current drops to zero.

The Open Circuit

€ The applied voltage is measured across

the open component.

Circuit Faults: The Short Circuit

€ A short circuit is the opposite of an open.

€ A short circuit is an unintentional low-

resistance connection between two points.

… This results in higher than normal current andusually results in a

fuse opening or

circuit breaker

tripping.

ENERGY

€ For power, which is the rate of doing work,to produce an energy conversion of anyform, it must be used over a period of time.

€ The energy (W ) lost or gained by any

system is therefore determined by:

ENERGY

€ Note that the energy in kilowatthours issimply the energy in watthours divided by1000.

€ To develop some sense for the

kilowatthour energy level, consider that 1kWh is the energy dissipated by a 100 Wbulb in 10 h.

€ The kilowatthour meter is an instrumentfor measuring the energy supplied to the

residential or commercial user of electricity.

ENERGY

FIG. 4.16 Kilowatthour meters: (a) analog; (b) digital. (Courtesy of ABB Electric Metering

Systems.) 58

ENERGY

FIG. 4.17 Cost per kWh and average kWh per customer versus time.

(Based on data from Edison Electric Institute.)59

ENERGY

TABLE 4.1 Typical wattage ratings of some common household

items. 60

Efficiency

€ The efficiency of a circuit is the ratio of input

power to output power, usually expressed as a

ratio.

€ It is defined mathematically as

%100ƒ€

EFFICIENCY

€ A flowchart for the energy levels

associated with any system that converts

energy from one form to another is

provided in Fig. 4.18.

€ Note that the output energy level mustalways be less than the applied energy due

to losses and storage within the system.

€ The best one can hope for is that W out and

W in are relatively close in magnitude.

EFFICIENCY

€ Conservation of energy requires that

… Energy input = energy output + energy lost

or stored by the system

FIG. 4.18 Energy flow through a system. 63

EFFICIENCY

FIG. 4.19 Basic components of a generating system. 64

EFFICIENCY

FIG. 4.20 Cascaded system.

CIRCUIT BREAKERS, GFCIs, AND

€ The incoming power to any large industrialplant, heavy equipment, simple circuit inthe home, or meters used in the laboratorymust be limited to ensure that the currentthrough the lines is not above the rated

value.€ To limit the current level, fuses or circuit

breakers are installed where the powerenters the installation, such as in the panelin the basement of most homes at the point

where the outside feeder lines enter thedwelling.

FIG. 4.21 Fuses: (a) CC-TRON• (0‚10 A); (b) Semitron (0‚600 A); (c)

subminiature surface-mount chip fuses.

€ In homes built in recent years, fuseshave been replaced by circuitbreakers.

€ When the current exceeds ratedconditions, an electromagnet in thedevice will have sufficient strength todraw the connecting metallic link inthe breaker out of the circuit and open

the current path.

FIG. 4.22 Circuit

breakers.

€ The most recentNational ElectricalCode (NEC)/PhilippineElectrical Code (PEC)requires that outlets in

the bathroom andother sensitive areasbe of the ground faultcircuit interrupt (GFCI)variety; GFCIs aredesigned to trip more

quickly than thestandard circuitbreaker.

FIG. 4.23 Ground fault circuitinterrupter (GFCI): 125 V ac, 60 Hz, 15

A outlet.

Applications: Electric Lighting

IncandescentLamp

Compact Fluorescent Lamp (CFL)

bulbs.com sciencetablets.blogspot.com

Light Emitting Diode (LED) Lamp

ecnmag.com

rootsbd.com

flexflireleds.com

spie.org76

micro.rohm.com 77

APPLICATIONSMicrowave Oven

FIG. 4.26 Microwave

APPLICATIONSHousehold Wiring

€ The one specification that defines the overallsystem is the maximum current that can be drawnfrom the power lines since the voltage is fixed at120 V or 240 V (sometimes 208 V).

€ For most older homes with a heating system other

than electric, a 100 A service is the norm.€ Today, with all the electronic systems becoming

commonplace in the home, many people areopting for the 200 A service even if they do nothave electric heat.

APPLICATIONSHousehold Wiring

FIG. 4.27 200 A service conductors: (a) 4/0 aluminum and 2/0 copper; (b)

three-wire 4/0 aluminum service.

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