Chapter 33 OhmOhm ’’ss LawLaw

Topics Covered in Chapter 3 3-1: The Current I = V/R 3-2: The Voltage V = IR 3-3: The Resistance R = V/I 3-4: Practical Units 3-5: Multiple and Submultiple Units

© 2007 The McGraw-Hill Companies, Inc. All rights reserved. TopicsTopics CoveredCovered inin ChapterChapter 33

3-6: The Linear Proportion between V and I 3-7: Electric Power 3-8: Power Dissipation in Resistance 3-9: Power Formulas 3-10: Choosing a Resistor for a Circuit 3-11: Electric Shock 3-12: Open-Circuit and Short-Circuit Troubles

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Ohm's law states that, in an electrical circuit, the current passing through most materials is directly proportional to the potential difference applied across them. 33--11——33--3:3: OhmOhm ’’ss LawLaw FormulasFormulas

There are three forms of Ohm’s Law: I = V/R V = IR R = V/I where: I = Current V = Voltage R = Resistance

Fig. 3-4: A circle diagram to help in memorizing the Ohm’s Law formulas V = IR, I = V/R , and R= V/I . The V is always at the top.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 33--1:1: TheThe CurrentCurrent II == V/RV/R

I = V/R In practical units, this law may be stated as: amperes = volts / ohms

Fig. 3-1: Increasing the applied voltage V produces more current I to light the bulb with more intensity.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 33--4:4: PracticalPractical UnitsUnits

The three forms of Ohm’s law can be used to define the practical units of current, voltage, and resistance: 1 ampere = 1 volt / 1 ohm 1 volt = 1 ampere × 1 ohm 1 ohm = 1 volt / 1 ampere 33--4:4: PracticalPractical UnitsUnits

Applying Ohm’s Law V ? I R 20 V 20 V 4 Ω I = = 5 A 4 Ω 1 A

? 12 Ω V = 1A × 12 Ω = 12 V

3 A 6 V 6 V ? R = = 2 Ω 3 A ProblemProblem

Solve for the resistance, R, when V and I are known a. V = 14 V, I = 2 A, R = ? b. V = 25 V, I = 5 A, R = ? c. V = 6 V, I = 1.5 A, R = ? d. V = 24 V, I = 4 A, R = ? 33--5:5: MultipleMultiple andand SubmultipleSubmultiple UnitsUnits

Units of Voltage The basic unit of voltage is the volt (V). Multiple units of voltage are: kilovolt (kV) 1 thousand volts or 10 3 V megavolt (MV) 1 million volts or 10 6 V Submultiple units of voltage are: millivolt (mV) 1-thousandth of a volt or 10 -3 V microvolt ( µV) 1-millionth of a volt or 10 -6 V 33--5:5: MultipleMultiple andand SubmultipleSubmultiple UnitsUnits

Units of Current The basic unit of current is the ampere (A). Submultiple units of current are: milliampere (mA) 1-thousandth of an ampere or 10 -3 A microampere ( µA) 1-millionth of an ampere or 10 -6 A 33--5:5: MultipleMultiple andand SubmultipleSubmultiple UnitsUnits

Units of Resistance The basic unit of resistance is the Ohm ( Ω). Multiple units of resistance are: kilohm (k Ω) 1 thousand ohms or 10 3 Ω Megohm (M Ω) 1 million ohms or 10 6 Ω ProblemProblem

How much is the current, I, in a 470-kΩ resistor if its voltage is 23.5 V?

How much voltage will be dropped across a 40 k Ω resistance whose current is 250 µA? 33--6:6: TheThe LinearLinear ProportionProportion betweenbetween VV andand II The Ohm’s Law formula I = V/R states that V and I are directly proportional for any one value of R.

Fig. 3.5: Experiment to show that I increases in direct proportion to V with the same R. ( a) Circuit with variable V but constant R. ( b) Table of increasing I for higher V. (c) Graph of V and I values. This is a linear volt-ampere characteristic. It shows a direct proportion between V and I. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 33--6:6: TheThe LinearLinear ProportionProportion betweenbetween VV andand II

When V is constant: I decreases as R increases. I increases as R decreases. Examples: If R doubles, I is reduced by half. If R is reduced to ¼, I increases by 4. This is known as an inverse relationship . 33--6:6: TheThe LinearLinear ProportionProportion betweenbetween VV andand II

Linear Resistance A linear resistance has a constant value of ohms. Its R does not change with the applied voltage, so V and I are directly proportional.

Carbon-film and metal-film resistors are examples of linear resistors. 33--6:6: TheThe LinearLinear ProportionProportion betweenbetween VV andand II

1 Ω 2 Ω 4 3 + 4 Ω 2 0 to 9 Volts 2 Ω Amperes _ 1

0 1 2 3 4 5 6 7 8 9 Volts The smaller the resistor, the steeper the slope. 33--6:6: TheThe LinearLinear ProportionProportion betweenbetween VV andand II

Nonlinear Resistance In a nonlinear resistance, increasing the applied V produces more current, but I does not increase in the same proportion as the increase in V. Example of a Nonlinear Volt–Ampere Relationship: As the tungsten filament in a light bulb gets hot, its resistance increases. Amperes Amperes

Volts 33--6:6: TheThe LinearLinear ProportionProportion betweenbetween VV andand II

Another nonlinear resistance is a thermistor. A thermistor is a resistor whose resistance value changes with its operating temperature. As an NTC (negative temperature coefficient) thermistor gets hot, its resistance decreases.

Thermistor Amperes Amperes

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Volts 33--7:7: ElectricElectric PowerPower

The basic unit of power is the watt (W). Multiple units of power are: kilowatt (kW): 1000 watts or 10 3 W megawatt (MW): 1 million watts or 10 6 W Submultiple units of power are: milliwatt (mW): 1-thousandth of a watt or 10 -3 W microwatt ( µW): 1-millionth of a watt or 10 -6 W 33--7:7: ElectricElectric PowerPower

Work and energy are basically the same, with identical units.

Power is different. It is the time rate of doing work. Power = work / time. Work = power × time. 33--7:7: ElectricElectric PowerPower

Practical Units of Power and Work: The rate at which work is done (power) equals the product of voltage and current. This is derived as follows: First, recall that:

1 joule 1 coulomb 1 volt = and 1 ampere = 1 coulomb 1 second 33--7:7: ElectricElectric PowerPower

Power = Volts × Amps, or P = V × I

1 joule 1 coulomb 1 joule Power (1 watt) = × = 1 coulomb 1 second 1 second 33--7:7: ElectricElectric PowerPower

Kilowatt Hours The kilowatt hour (kWh) is a unit commonly used for large amounts of electrical work or energy.

For example, electric bills are calculated in kilowatt hours. The kilowatt hour is the billing unit.

The amount of work (energy) can be found by multiplying power (in kilowatts) × time in hours. 33--7:7: ElectricElectric PowerPower

To calculate electric cost, start with the power: An air conditioner operates at 240 volts and 20 amperes. The power is P = V × I = 240 × 20 = 4800 watts. Convert to kilowatts : 4800 watts = 4.8 kilowatts Multiply by hours : (Assume it runs half the day) energy = 4.8 kW × 12 hours = 57.6 kWh Multiply by rate : (Assume a rate of $0.08/ kWh) cost = 57.6 × $0.08 = $4.61 per day ProblemProblem

How much is the output voltage of a power supply if it supplies 75 W of power while delivering a current of 5 A?

How much does it cost to light a 300-W light bulb for 30 days if the cost of the electricity is 7¢/kWh. 33--8:8: PowerPower DissipationDissipation inin ResistanceResistance

When current flows in a resistance, heat is produced from the friction between the moving free electrons and the atoms obstructing their path.

Heat is evidence that power is used in producing current. 33--8:8: PowerPower DissipationDissipation inin ResistanceResistance

The amount of power dissipated in a resistance may be calculated using any one of three formulas, depending on which factors are known: P = I 2×R P = V 2 / R P = V×I ProblemProblem

Solve for the power, P, dissipated by the resistance, R a. I = 1 A, R = 100 Ω , P = ? b. I = 20 mA, R = 1 k Ω , P = ? c. V = 5 V, R = 150 Ω , P = ? d. V = 22.36 V, R = 1 k Ω , P = ?

How much power is dissipated by an 8-Ω load if the current in the load is 200 mA? 33--9:9: PowerPower FormulasFormulas

There are three basic power formulas, but each can be in three forms for nine combinations. V2 P = VI P = I 2R P = R

P P 2 I = R = V V 2 R = I P P P V = I = V= PR I R

Where: P = Power V = Voltage I = Current R=Resistance 33--9:9: PowerPower FormulasFormulas

Combining Ohm’s Law and the Power Formula All nine power formulas are based on Ohm’s Law. V = IR P = VI I = V R

Substitute IR for V to obtain: P = VI = (IR)I = I 2R 33--9:9: PowerPower FormulasFormulas

Combining Ohm’s Law and the Power Formula Substitute V/R for I to obtain: P = VI = V × V/ R = V 2 / R 33--9:9: PowerPower FormulasFormulas

Applying Power Formulas:

5 A P = VI = 20 × 5 = 100 W 20 V 4 ΩΩΩ P = I 2R = 25 × 4 = 100 W V2 400 P = = = 100 W R 4 ProblemProblem

What is the resistance of a device that dissipates 1.2 kW of power when its current is 10 A?

How much current does a 960 W coffeemaker draw from the 120 V power line?

What is the resistance of a 20 W, 12 V halogen lamp? 33--10:10: ChoosingChoosing aa ResistorResistor forfor aa CircuitCircuit

Follow these steps when choosing a resistor for a circuit: Determine the required resistance value as R = V / I. Calculate the power dissipated by the resistor using any of the power formulas. Select a wattage rating for the resistor that will provide an adequate cushion between the actual power dissipation and the resistor’s power rating. Ideally, the power dissipation in a resistor should never be more than 50% of its power rating. ProblemProblem

Determine the required resistance and appropriate wattage rating of a carbon-film resistor to meet the following requirements. The resistor has a 54-V IR drop when its current is 20 mA. The resistors available have the following wattage ratings: 1/8 W, 1/4 W, 1/2 W, 1 W, and 2 W. 33--10:10: ChoosingChoosing aa ResistorResistor forfor aa CircuitCircuit

Maximum Working Voltage Rating A resistor’s maximum working voltage rating is the maximum voltage a resistor can withstand without internal arcing.

The higher the wattage rating of the resistor, the higher the maximum working voltage rating. 33--10:10: ChoosingChoosing aa ResistorResistor forfor aa CircuitCircuit

Maximum Working Voltage Rating With very large resistance values, the maximum working voltage rating may be exceeded before the power rating is exceeded.

For any resistor, the maximum voltage which produces the rated power dissipation is: V max = Prating × R

Exceeding Vmax causes the resistor’s power dissipation to exceed its power rating 33--11:11: ElectricElectric ShockShock

When possible, work only on circuits that have the power shut off.

If the power must be on, use only one hand when making voltage measurements.

Keep yourself insulated from earth ground.

Hand-to-hand shocks can be very dangerous because current is likely to flow through the heart! 33--12:12: OpenOpen --CircuitCircuit andand ShortShort --CircuitCircuit TroublesTroubles

An open circuit has zero current flow.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 33--12:12: OpenOpen --CircuitCircuit andand ShortShort --CircuitCircuit TroublesTroubles

A short circuit has excessive current flow.

As R approaches 0, I approaches ∞.

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