electric currents and ohm’s la · • electric forces & ﬁelds; coulomb’s law &...

CollegePhysics B

ElectricCurrents

Ohm’s LawResistance

Electric Power

Transmission Voltage

ElectricCircuitsResistors in Series

Resistors in Parallel

Superconductivity

College Physics B - PHY2054C

Electric Currents and Ohm’s Law

09/15/2014

My Office Hours:Tuesday 10:00 AM - Noon

206 Keen Building

CollegePhysics B

ElectricCurrents


Electric Power




Superconductivity

PHY2054C

First Mini-Exam this week on Wednesday!!• Location: UPL 101, 10:10 - 11:00 AM

• Exam on chapters 19, 20 & 21• Electric forces & fields; Coulomb’s Law & Gauss’s Law• Electric potential & electric potential energy• Electric current, resistors & capacitors

• Equation sheet will be provided.

• Do not forget to bring your student ID!

CollegePhysics B

ElectricCurrents


Electric Power




Superconductivity

Review: Electric Potential

The electric potential V is proportional to the electric potential energy.

If the electric potential energy of a charge q at a particular location isPEelec, the electric potential at that point is

V =PE elec

q.

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Electric Power




Superconductivity

Review: Electric potential

The electric potential V is proportional to the electric potential energy.

Suppose the potential changes by an amount ∆V over a distance∆x . The component of the electric field along this direction is then

E = −∆V∆x

.

CollegePhysics B

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Superconductivity

Capacitance

Electric Potential of a capacitor:

E =Q

ǫ0 A=

∆Vd

∆V =Q dǫ0 A

= E d

Capacitance C is defined as:

∆V =QC

C =ǫ0 Ad

”Parallel-Plate Capacitor”

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Superconductivity

Review Question 1

phet.colorado.edu/en/simulation/capacitor-lab

Four 16 µF capacitors are connected in series. The equivalentcapacitance of this combination is

A 64.0 µF

B 16.0 µF

C 4.0 µF

D 2.0 µF


CollegePhysics B

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Superconductivity

Review Question 1


Four 16 µF capacitors are connected in series. The equivalentcapacitance of this combination is

A 64.0 µF

B 16.0 µF

C 4.0 µF

D 2.0 µF

When two capacitors are connected in series, they act as asingle equivalent capacitance with a value

1Cequiv

=1

C1+

1C2

and Q = Q1 = Q2


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Review Question 2


Four 16 µF capacitors are now connected in parallel. Theequivalent capacitance of this combination is

A 64.0 µF

B 16.0 µF

C 4.0 µF

D 2.0 µF


CollegePhysics B

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Superconductivity

Review Question 2


Four 16 µF capacitors are now connected in parallel. Theequivalent capacitance of this combination is

A 64.0 µF

B 16.0 µF

C 4.0 µF

D 2.0 µF

When two capacitors are connected in parallel, they act as asingle equivalent capacitance with a value

Cequiv = C1 + C2 and Q = Q1 + Q2


CollegePhysics B

ElectricCurrents


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Superconductivity

Outline

1 Electric Currents

2 Ohm’s LawResistanceElectric PowerTransmission Voltage

3 Electric CircuitsResistors in SeriesResistors in ParallelSuperconductivity

CollegePhysics B

ElectricCurrents


Electric Power




Superconductivity

Electric Current

The motion of charges leads tothe idea of electric circuits:

• Electric current, I, in a wire isdefined as the net amount ofcharge that passes through itper unit time at any point:

I =∆Q∆t

• The unit of electric current:[

Cs

]

= [ A ] Ampere

• Current is defined in terms ofnet positive charge flow.

CollegePhysics B

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Electric Power




Superconductivity

Electric Current

André-Marie Ampère(22 January 1775 - 10 June 1836)

Electric current is the flow of electric charge (a phenomenon)or the rate of flow of electric charge (a quantity). This flowingelectric charge is typically carried by moving electrons, in aconductor such as wire; in an electrolyte, it is instead carriedby ions, and, in a plasma, by both.

CollegePhysics B

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Superconductivity

Direction of the Current

+ -

current flow

device

[battery symbol]

CollegePhysics B

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Superconductivity

Direction of the Current

1 If the current is carried by positive charges moving with agiven velocity, the direction of the current is parallel to thevelocity.

2 If the current is carried by negative charges, the directionof the current is opposite the charges’ velocity.

CollegePhysics B

ElectricCurrents


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Superconductivity

Current and Potential Energy

For charge to move along a wire, the electric potential energyat one end of the wire must be higher than the electric potentialenergy at the other end.

• Electric potential is relatedto electric potential energy:

V = PEelec / q

• The potential is referred tosimply as “voltage”.

• The direction of I is alwaysfrom high to low potential,regardless if the current iscarried by + or − charges.

CollegePhysics B

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Simple Circuit

If the battery terminals are connected to two ends of a wire, acurrent is produced:

• Electrons move out of the negative terminal of the batterythrough the wire and into the positive battery terminal.

• The chemical reaction moves charge internally betweenthe electrodes.

• No net charge accumulates on the battery terminals whilethe current is present.

• Battery will “run down”.

CollegePhysics B

ElectricCurrents


Electric Power




Superconductivity

Outline

1 Electric Currents



CollegePhysics B

ElectricCurrents


Electric Power




Superconductivity

Ohm’s Law

V

I

ohmic device

slope = R

1 Drag force on electrons leads to a drift velocity proportionalto the force pushing the electrons.

2 Force is proportional to the electric field, so the drift velocityis proportional to the field.

3 The electric field is proportional to the potential difference,so the drift velocity is proportional to the potential difference.

4 The current is proportional to the drift velocity, so the currentis proportional to the potential difference:

I =VR

Ohm′s Law

Unit of Resistance R :

[

VA

]

= [Ω ]

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Superconductivity

Ohm’s Law

George Simon Ohm(16 March 1789 - 6 July 1854)

Ohm’s law states that the current through a conductor betweentwo points is directly proportional to the potential difference orvoltage across the two points, and inversely proportional to theresistance between them.

Ohm’s Law:http://phet.colorado.edu/sims/ohms-law/ohms-law_en.html

http://phet.colorado.edu/sims/ohms-law/ohms-law_en.html

CollegePhysics B

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Superconductivity

Resistivity

The resistivity, ρ, depends only on the material used to makethe wire. Resistance of a wire of length L and cross sectionalarea A is given by:

R = ρLAMaterial ρ [ Ω · m ]

Copper 1.7 × 10−8

Glass 1 to 1000 × 109

Silicon 0.1 to 100

CollegePhysics B

ElectricCurrents


Electric Power




Superconductivity

Resistors

All electronic devices, from heaters to light bulbs to stereoamplifiers, offer resistance to the flow of current and aretherefore considered resistors.

• Resistors can be made inmany shapes and sizes.

• Each will have a resistanceproportional to the currentthrough and the potentialacross the resistor.

Many, but not all, materials and devices obey Ohm’s Law. Ohm’s Law is not a fundamental law of nature.

Resistors do obey Ohm’s Law.

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Superconductivity

Circuit Schematic

• The circuit diagram (A) showsthe symbols for the resistorand the battery.

• Since the resistance of thewires is much smaller thanthat of the resistors, a goodapproximation is Rwire = 0.

• If the circuit is open, there isno current flow anywhere inthe circuit.

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Circuit Symbols

CollegePhysics B

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Superconductivity

Electric Power

Reminder:Ohm’s Law: R = V / I

Energy in a Resistor

• The test charge gained energy when it passed through thebattery.

• It lost energy as it passed through the resistor.

• Energy is converted into heat energy inside the resistor:

• The energy is dissipated as heat.

• It shows up as a temperature increase of the resistor and itssurroundings.

P (Power) =energy transformed

time=

Q Vt

= I V

P = I V = I 2 R = V 2 / R

Electric Power

CollegePhysics B

ElectricCurrents


Electric Power




Superconductivity

Resistance of a Light Bulb

What is a typical household light bulb? 60 Watt light bulb

What is a typical household voltage? 110 Volts

What else do we know? P = V I = V 2 / R

R =V 2

P=

(110 V)2

60 W≈ 200 Ω

Battery-Resistor Circuit:phet.colorado.edu/en/simulation/battery-resistor-circuit

phet.colorado.edu/en/simulation/battery-resistor-circuit

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Question 3

Hint: Think about

P = V I = V 2 / R

In the US and Canada, the standard line voltage isVRMS = 110 V. In much of the world (Europe, Australia,Asia), the standard line voltage is VRMS = 220 V.

The light output of a 60 Watt Tallahassee light bulb ifused in Europe would

A be twice as bright.

B be four times as bright.

C be half as bright.

D be one fourth as bright.

E remain the same brightness.

CollegePhysics B

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Superconductivity

Question 3



A be twice as bright.

B be four times as bright. P = V I = V 2 / R

C be half as bright. It must get brighter.

D be one fourth as bright.

E remain the same brightness.

CollegePhysics B

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Superconductivity

Question 3



B be four times as bright. P = V I = V 2 / R

How much brighter?

P Europe

V 2Europe

=

1R

=

P USA

V 2USA

→ P Europa = P USA ·V 2

Europe

V 2USA

P Europa = 4 P USA

CollegePhysics B

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Electric Power




Superconductivity


Plost = I 2 R and P = V I

Plost =

(

PD

VD

)2

R → High Voltage is Better.

CollegePhysics B

ElectricCurrents


Electric Power




Superconductivity

Incandescent Lamps

Electric lightbulbs are rated in watts.

Incandescent lamps are relatively inefficient as light sources.

• Typically, less than 5 % of the electrical energy isconverted to visible light.

• Most of the energy produced is invisible infraredradiation and heat (resistive heating).

CollegePhysics B

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Superconductivity

Incandescent Lamps

Electric lightbulbs are rated in watts.

Incandescent lamps are relatively inefficient as light sources.

• Typically, less than 5 % of the electrical energy isconverted to visible light.

• Most of the energy produced is invisible infraredradiation and heat (resistive heating).

New technologies have greatly reduced the watts, saving thelumens: Halogen, compact fluorescent, LED.

CollegePhysics B

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Superconductivity

Resistivity & Temperature

Resistance of a metal wire: R = ρ LA

In general, the resistance of metal increases with temperature:

ρT = ρ0 [ 1 + α (T − T0) ]

Temperature Coefficients

Material α [ (C)−1 ]

Silver 0.0061

Copper 0.0068

Silicon −0.07

CollegePhysics B

ElectricCurrents


Electric Power




Superconductivity

Outline

1 Electric Currents



CollegePhysics B

ElectricCurrents


Electric Power




Superconductivity

Resistors in Series

When current passes through one resistor and then another,the resistors are said to be in series:

E − I R 1 − I R 2 = 0 Kirchhoff ′s Loop Rule

Any number of resistors can be connected in series. Theresistors will be equivalent to a single resistor with:

R equiv = R 1 + R 2 + R 3 + ...

CollegePhysics B

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Superconductivity


In some circuits, the current can take multiple paths:

• The different paths are called branches.

• The arrangement of resistors shown is called resistors inparallel.

• Amount of current entering a junction must be equal tothe current leaving it.

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Superconductivity


Applying the Junction Rule (Kirchhoff ’s Junction Rule)

For path 1, +E − I 1 R 1 = 0

For path 2, +E − I 2 R 2 = 0

The total current is: I 3 = I 1 + I 2 = E

R 1+ E

R 2= E ( 1

R 1+ 1

R 2)

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Superconductivity

Equivalent Resistance - Parallel

CollegePhysics B

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Circuit Analysis

1 Some complex circuits can be solved by combinations ofseries and parallel rules.

2 Other circuits must be analyzed directly by Kirchhoff’s Rules.

• Loop Rule: The total change in the electric potential aroundany closed circuit path must be zero.

• Junction Rule: The current entering a circuit junction mustequal the current leaving the junction.

3 Connecting resistors in series always gives a total resistancelarger than the resistance of any of the component resistors.

4 Connecting resistors in parallel always gives a totalresistance smaller than the resistance of any of thecomponent resistors.

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Ammeters

An Ammeter is a device thatmeasures current.

• An ammeter must be connected in series with thedesired circuit branch.

• An ideal ammeter will measure current without changingits value. Must have a very low resistance.

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Superconductivity

Voltmeters

A Voltmeter is a device thatmeasures the voltage acrossa circuit element.

• It must be connected in parallel with the element.

• An ideal voltmeter should measure the voltage withoutchanging its value. Should have a very high resistance.

CollegePhysics B

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Electric Power




Superconductivity

Electric Currents and Nerves

Many nerves are long and thin, much like wires.

• The conducting solution inside the fiber acts as a resistor.

• The lipid layer acts as a capacitor.

• The nerve fiber behaves as an RC circuit. More on RC circuits next week!

Your body is a moderately good conductor of electricity.

• The body’s resistance when dry is about 1500 Ω.

• When wet, the body’s resistance is about 500 Ω.

• Current is carried by different parts of the body:Skin, internal organs, ...

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Electric Power




Superconductivity

Superconductivity

At very low temperatures, thelinearity of resistance breaksdown.

• The resistivities of metalsapproach a nonzero valueat very low temperatures.

• In some metals, resistivitydrops abruptly and is zerobelow a criticaltemperature.

• These metals for whichthe resistivity goes tozero are the calledsuperconductors.

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Superconductivity

Superconductivity

John Robert SchriefferNobel LaureateEmeritus Professor at Florida State

Bardeen, Cooper, and Schrieffer received the Nobel Prize in1972 for the development of the theory of superconductivity.The BCS Theory is one of the greatest discoveries of the 20thcentury.

electric currents and ohm’s la · • electric forces & ﬁelds; coulomb’s law &...

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