electrical energy and currentsection 1 © houghton mifflin harcourt publishing company preview...

Electrical Energy and Current Section 1

Preview

Section 1 Electric Potential

Section 2 Capacitance

Section 3 Current and Resistance

Section 4 Electric Power

The student is expected to:TEKS

6B investigate examples of kinetic and potential

energy and their transformations

What do you think?

• You may have purchased batteries for radios, watches, CD players, and other electronic devices. Batteries come in a variety of different sizes and voltages. You probably have 1.5 volt, 3 volt, and 12 volt batteries in your home.• What do volts measure?• Is the number of volts related to the size of the

battery?• How is a 3 volt battery different from a 1.5 volt

battery?

Electrical Potential Energy

• A uniform electric field exerts a force on a charged particle moving it from A to B.

• Will the particle shown gain or lose PEelectric as it moves to the right?– Lose energy (because it is moving

with the force, not against it)

– Similar to a falling object losing PEg

PEelectric = Wdone = Fd = -qED

PEelectric is positive if the charge is negative and moves with the field.

PEelectric is positive if the charge is positive and moves against the field.

Classroom Practice Problem

• A uniform electric field strength of 1.0 x 106 N/C exists between a cloud at a height of 1.5 km and the ground. A lightning bolt transfers 25 C of charge to the ground. What is the change in PEelectric for this lightning bolt?

• Answer: -3.75 x 1010 J of energy

Gravitational Potential Difference• Suppose a mass of 2.00 kg is moved from point A

straight up to point B a distance of 3.00 m. Find the PEg for the mass if g = 9.81 m/s2. Repeat for a mass of 5.00 kg.– Answer: 58.9 J and 147 J

• What is the PEg per kg for each?– Answer: 29.4 J/kg for both

• The change per kg does not depend on the mass. It depends only on points A and B and the field strength.

• There is an analogous concept for electrical potential energy, as shown on the next slide.

Potential Difference• Potential difference (V) is the change in electrical

potential energy per coulomb of charge between two points.– Depends on the electric field and on the initial and final positions– Does not depend on the amount of charge– SI unit: joules/coulomb (J/C) or Volts (V)

Potential Difference

• The potential difference is calculated between two points, A and B.– The field must be uniform.

Click below to watch the Visual Concept.

Visual Concept

Potential Difference Near a Point Charge

• The above V determines the potential energy per coulomb at a point compared to a very distant point where V would equal zero.

• Potentials are scalars (+ or -) so the total potential at a point is the sum of the potentials from each charge.

Visual Concept

Superposition Principle and Electric Potential

Batteries

• A battery maintains a constant potential difference between the terminals.– 1.5 V (AAA, AA, C and D cell) or 9.0 V or 12 V (car)

• In 1.5 V batteries, the electrons use chemical energy to move from the positive to the negative terminal.– They gain 1.5 joules of energy per coulomb of charge

• When connected to a flashlight, the electrons move through the bulb and lose 1.5 joules of energy per coulomb of charge.

Now what do you think?

• You may have purchased batteries for radios, watches, CD players, and other electronic devices. Batteries come in a variety of different sizes and voltages. You probably have 1.5 volt, 3 volt, and 12 volt batteries in your home.– What do volts measure?– Is the number of volts related to the size of the

battery?– How is a 3 volt battery different from a 1.5 volt

battery?

What do you think?

• If a light bulb replaced the two metal plates and the battery was connected, electrons would flow out of the negative and into the positive terminal. Will this also occur with the two metal plates?• If not, why not?• If so, is the flow similar or different from that with the light bulb?

Explain.

• The battery shown has a potential difference of 6.0 volts. It has just been connected to two metal plates separated by an air gap. There is no electrical connection between the two plates and air is a very poor conductor.

Capacitors

• The two metal plates are electrically neutral before the switch is closed. What will happen when the switch is closed if the left plate is connected to the negative terminal of the battery?– Electrons will flow toward lower

PE.• From the battery to the left plate

• From the right plate to the battery

Parallel Plate Capacitors

• Electrons build up on the left plate, giving it a net negative charge. The right plate has a net positive charge.– Capacitors can store charge or electrical PE.

Visual Concept

Capacitance

Capacitance• Capacitance measures the ability to store charge.

• SI unit: coulombs/volt (C/V) or farads (F)• In what way(s) is a capacitor like a battery?• In what way(s) is it different?

Capacitance

• How would capacitance change if the metal plates had more surface area?– Capacitance would increase.

• How would it change if they were closer together?– Capacitance would increase.

Capacitance

is a constant that is determined by the material between the plates (0 refers to a vacuum).

• Combining the two equations for C yields:

Visual Concept

Parallel-Plate Capacitor

Dielectrics

• The space between the plates is filled with a dielectric.– Rubber, waxed paper, air

• The dielectric increases the capacitance.– The induced charge on

the dielectric allows more charge to build up on the plates.

Capacitor Applications

• Connecting the two plates of a charged capacitor will discharge it.– Flash attachments on cameras use a

charged capacitor to produce a rapid flow of charge.

• Some computer keyboards use capacitors under the keys to sense the pressure.– Pushing down on the key changes the

capacitance, and circuits sense the change.

Energy and Capacitors

• As the charge builds, it requires more and more work to add electrons to the plate due to the electrical repulsion. – The average work or PE stored in the capacitor is (1/2)QV.

– Derive equivalent equations for PEelectric by substituting:

Q = CV and V = Q/C

Classroom Practice Problem

• A 225 F is capacitor connected to a 6.00 V battery and charged. How much charge is stored on the capacitor? How much electrical potential energy is stored on the capacitor?– Answers: 1.35 x 10-3 C , 4.05 x 10-3 J

• If a light bulb replaced the two metal plates and the battery was connected, electrons would flow out of the negative and into the positive terminal. Will this also occur with the two metal plates?• If not, why not?• If so, is the flow similar or

different from that with the light bulb? Explain.

5E characterize materials as conductors or insulators

based on their electrical properties

What do you think?

• The term resistance is often used when describing components of electric circuits.• What behavior of the components

does this term describe?• Do conductors have resistance?

• If so, are all conductors the same? Explain.

• What effect would increasing or decreasing the resistance in a circuit have on the circuit?

Electric Current

• Electric current (I) is rate at which charges flow through an area.

• SI unit: coulombs/second (C/s) or amperes (A)– 1 A = 6.25 1018 electrons/second

Conventional Current

• Conventional current (I) is defined as the flow of positive charge.– The flow of negative charge

as shown would be equivalent to an equal amount of positive charge in the opposite direction.

• In conducting wires, I is opposite the direction of electron flow.

Visual Concept

Conventional Current

Velocity of Electrons Through Wires

• When you turn on a wall switch for a light, electrons flow through the bulb. Which speed below do you believe most closely approximates that of the electrons?– The speed of light (300 000 000 m/s)– 1 000 m/s– 10 m/s– 0.0001 m/s

• Why do you think so?

Drift Velocity• Electrons undergo

collisions with atoms in the metal.– They “drift” through the wire.– Drift velocity for a copper

wire with a current of 10 A is 0.000246 m/s.

• The E field moves through the wire near the speed of light, causing all electrons in the wire to move nearly instantly.

Visual Concept

Drift Velocity

Resistance to Current• Resistance is opposition to the flow of charge.

– SI unit: volts/ampere (V/A) or ohms ()

• Ohm’s Law : V = IR– Valid only for certain materials whose resistance is constant

over a wide range of potential differences

Classroom Practice Problems

• A typical 100 W light bulb has a current of 0.83 A. How much charge flows through the bulb filament in 1.0 h? How many electrons would flow through in the same time period?– Answers: 3.0 103 C, 1.9 1022 electrons

• This same 100 watt bulb is connected across a 120 V potential difference. Find the resistance of the bulb.– Answer: 1.4 102

Resistance of a Wire

• On the next slide, predict the change necessary to increase the resistance of a piece of wire with respect to:– Length of wire– Cross sectional area or thickness of the wire– Type of wire– Temperature of the wire

Visual Concept

Factors that Affect Resistance

Applications

• Resistors in a circuit can change the current.– Variable resistors (potentiometers) are used in

dimmer switches and volume controls.– Resistors on circuit boards control the current to

components.

• The human body’s resistance ranges from 500 000 (dry) to 100 (soaked with salt water).– Currents under 0.01 A cause tingling.– Currents greater than 0.15 A disrupt the heart’s

electrical activity.

• The term resistance is often used when describing components of electric circuits.• What behavior of the components

does this term describe?• Do conductors have resistance?

• If so, are all conductors the same? Explain.

• What effect would increasing or decreasing the resistance in a circuit have on the circuit?

What do you think?

• Hair dryers, microwaves, stereos, and other appliances use electric power when plugged into your outlets.• What is electric power?

• Is electric power the same as the power discussed in the chapter “Work and Energy?”

• Do the utility companies bill your household for power, current, potential difference, energy, or something else?

• What do you think is meant by the terms alternating current (AC) and direct current (DC)?

• Which do you have in your home?

Types of Current - Direct

• Batteries use chemical energy to give electrons potential energy.– Chemical energy is eventually depleted.

• Electrons always flow in one direction.– Called direct current (DC)

Types of Current - Alternating

• Generators change mechanical energy into electrical energy.– Falling water or moving steam

• Electrons vibrate back and forth.– Terminals switch signs 60 times

per second (60 Hz).– Called alternating current (AC)– AC is better for transferring

electrical energy to your home.

Energy Transfer

• Is the electrical potential energy gained, lost, or unchanged as the electrons flow through the following portions of the circuit shown: – A to B– B to C– C to D– D to A

• Explain your answers.

Energy Transfer– A to B (unchanged)– B to C (lost in bulb)– C to D (unchanged)– D to A (gained in battery)

Visual Concept

Electric Power

• Power is the rate of energy consumption (PE/t ). For electric power, this is equivalent to the equation shown below.– SI unit: joules/second (J/S) or watts (W)

– Current (I) is measured in amperes (C/s).

– Potential difference (V) is measured in volts (J/C).

• Substitute using Ohm’s law (V = IR) to write two other equations for electric power.

Classroom Practice Problems

• A toaster is connected across a 120 V kitchen outlet. The power rating of the toaster is 925 W.– What current flows through the toaster?– What is the resistance of the toaster?– How much energy is consumed in 75.0 s?

• Answers: 7.7 A, 16 , 6.94 104 J

Household Energy Consumption

• Power companies charge for energy, not power.– Energy consumption is measured in kilowatt•hours

( kw•h).• The joule is too small.

– A kw•h is one kilowatt of power for one hour.• Examples of 1 kw•h:

– 10 light bulbs of 100 W each on for 1 h

– 1 light bulb of 100 W on for 10 h

• 1 kw•hr = 3 600 000 J or 3.6 x 106 J

Visual Concept

Relating Kilowatt-Hours to Joules

Electrical Energy Transfer

• Transfer of energy from power plants to your neighborhood must be done at high voltage and low current.– Power lost in electrical lines is significant.

• P = I2R• Power lines are good conductors but they are very long.• Since power companies can’t control the resistance (R), they

control the current (I) by transferring at high voltage.

• Hair dryers, microwaves, stereos, and other appliances use electric power when plugged into your outlets.– What is electric power?

• Is electric power the same as the power discussed in the chapter “Work and Energy?”

– Do the utility companies bill your household for power, current, potential difference, energy, or something else?

– What do you think is meant by the terms alternating current (AC) and direct current (DC)?

• Which do you have in your home?

electrical energy and currentsection 1 © houghton mifflin harcourt publishing company preview...

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