Alta Physics

Chapters 16 - 19

Electrical Energy, Electric Fields

& DC Circuits

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Other Forms of Stored Energy:

Chemical Energy Stored in the Chemical Bonds that

make up a substance Often released by combustion (burning) Released as

kinetic energy Heat Light Sound

*** Demonstration ***

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Electric Charge and Electric Field

Static Electricity – Unmoving charge Two types

Positive – lack of electrons Negative – excess electrons

Like charges - Repel Opposite Charges - Attract

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Electric Charges Charge can be induced by rubbing

an object – View demonstrations

Charge is detected using an electroscope.

Charge can travel via a conductor. Poor conductors are insulators.

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Force Exerted by Charges Coulomb’s Law

F = kQ1Q2/r2

k = 9 x 109 N•m2/C2

Positive solution – repulsion Negative solution - attraction

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Sample Problem

Two charges, Q1 = +10 µC, and Q2 = -15 µC, are separated by 1.5 meters.

What is the electrostatic force acting between them?

SolutionF = kQ1Q2/r2 =

(9 x 109 N•m2/C2)(+10 x 10-6 C)(-15 x 10-6 C)/(1.5 m)2

= -0.6 N

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Electric Field Field – Affect that acts at a

distance, without contact Examples

Electric Field Gravitational Field

Electric Field Strength – E = F/q = kQ/r2

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Sample Problem

Calculate the strength of an electric field at a point 30 cm

from a point charge Q = +3 µC

SolutionE = kQ/r2 =

(9 x 109 N•m2/C2)(+3 x 10-6 C)/(0.3 m)2

= 300000 N/C

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Electrical Energy Electrical Energy is generated from other

forms of energy and transmitted over power lines and/or stored in batteries

Vocabulary Voltage (V)

Force in an electrical system; Volt = Work/Charge = W/q = Joule/Coloumb

Current (I) Rate in an electrical system = Charge/time = q/t

=Coloumb/sec = 1 Ampere

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Energy in Electrical System

Volts =Work/charge = V =W/q Work is measured in joules (the same

as energy) Charge is measured in Coloumbs (C) The charge on an electron is 1.6 x 10-

19 C 1 V = 1 Joule/1 Coloumb

Work = Volts * Charge = Vq

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Sample Problem How much work is needed to move

a 10 μC charge to a point where the potential is 70 V?

W = Vq = (70 V)(10 x 10-6 C) = 7 x 10-4 J

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Electrical Energy Storage Electrical Energy can be stored in two

ways: Batteries

Long term storage, even flow of charge Storage ability measured in Volts

Capacitors Short term storage, releases charge all at once (boost

in charge) Storage capacity measured in Farads (F) 1 Farad = 1 Coloumb/Volt Mathematically Charge = Capacitance * Voltage = q

= CV

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Sample Problem What charge is stored when a 0.5 F

capacitor is attached to a 9 volt source?

Solutionq = CV = (0.5 F)(9 V)

= 4.5 Coloumbs

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Capacitance To calculate the capacitance of a

plate capacitatorC = Kε0A/d

where K = the dielectric constant

ε0 = the permitivity constant 8.85 x 10-12 C2/N•m2

A = the area of the plates in m2

d = the distance between the plates in meters

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Sample Problem What is the capacitance of a capacitor

consisting of 2 plates, each having an area of 0.5 m2, separated by 2 mm of mica?

SolutionC = Kε0A/d

= (7)(8.85 x 10-12 C2/N•m2)(0.5 m2)/(.002 m)= 1.55 x 10-9 F = 1.55 nF

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An Old Equation – with a twist

Remember that the equation for the strength of an electric field is given by

E = F/Qnow we have

V = W/Q where W = F x dso

V/d = E or V = Ed

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Electric Current Circuit – A continuous path

connected between the terminals of a power source.

Current – Flow of Charge I = ΔQ/Δt Current is measured in

Coloumbs/Sec which is called an Ampere.

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Electric Current Electron Flow is from – terminal to

+ terminal. Conventional Current is from +

terminal to – terminal.

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Sample Problem

A steady current of 2.5 Amps passes through a wire for 4 minutes. How much charge passed through any point in

the circuit?Solution

Q = IΔt (2.5 C/s)(240 s) = 600 C

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Ohm’s Law Resistance – how much the

conductor slows down the flow of electrons through it.

Resistance is measured in Ohms (Ω)

Ohm’s law -In any Circuit:V = IR or R = V/I

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Sample Problem

A small flashlight bulb draws a current of 300 mA from a 1.5 V battery. What is the resistance

of the bulb?SolutionR = V/I =

(1.5 V)/(0.3 A) = 5 Ω

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Resistor Color Code Resistors are banded in order to

describe the amount of resistance they provide. Each resistor is banded with 4 stripes.

Band Represents

1 First Digit

2 Second Digit

3 Multiplier

4 Tolerance

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Bright Black 0

Boys Brown 1

Remember Red 2

Our Orange 3

Young Yellow 4

Girls Green 5

Become Blue 6

Very Violet 7

Good Grey 8

Wives White 9

Gold 5%

Silver 10%

None 20%

Resistor Color Code

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Sample Problem

Calculate the resistance of a resistor which is banded with the

following colors: Red, Green, Blue, Silver.Solution

Red = 2, Green = 5, Blue = 6 and Silver = 10% R = 25000000 ± 10%

OrR = 25 MΩ ± 10%

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Resistivity Spools or lengths of wire each have

their own Resistance. Resistivity of these items can be

calculated using the equation:R = ρL/A

Where ρ is a constant, L is length, and A is cross sectional area of the wire.

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Sample Problem

Calculate the resistance of a spool of

copper wire which is 20 m long andhas a cross sectional area of 3.4 x 10-6 m2?

SolutionR = ρL/A=

(1.68 x 10-8Ω•m)(20 m)/(3.4 x 10-6 m2) = 1.14 x 10-12 Ω

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DC Circuits Batteries Connected in Series

Increase Voltage Et= E1 + E2 + E3. . .

Produce the Same Current It= I1 = I2 = I3. . .

Batteries Connected in Parallel Produce the Same Voltage

Et= E1 = E2 = E3. . . Increase Current

It= I1 + I2 + I3. . .

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Sample Problem

Calculate the voltage and current when 3 batteries (1.5 V, 0.25 A are connected in

A) SeriesB) Parallel

Solutiona) Et= E1 + E2 + E3 =1.5 V + 1.5 V + 1.5 V = 4.5 V

It= I1 + I2 + I3= 0.25 A

b) Et= E1 = E2 = E3=1.5 V

It= I1 + I2 + I3=0.25 A + 0.25 A + 0.25 A = 0.75 A

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DC Circuits Resistance in Series

Rt=R1+R2+R3. . . Resistance in Parallel

...1111

321 RRRRt

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Sample ProblemCalculate the resistance when a 5 Ω, 6 Ω,

and 3 Ω resistor are connected in A) SeriesB) Parallel

Solution

a) Rt=R1+R2+R3 = 5 Ω+ 6 Ω+ 3 Ω = 14 Ωb)

Rt= 1.43 Ω

30

21

30

10

30

5

30

6

3

1

6

1

5

11111

321 RRRRt

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Problem Types Coloumb’s Law Electric Fields Voltage & Current Capacitors Circuits

Batteries Ohm’s Law Power