Physics 1502: Lecture 12 Today’s Agenda - phys.uconn.edu · Physics 1502: Lecture 12 Today’s Agenda ... an ammeter should have zero resistance so that ... An ideal voltmeter should

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Lecture 4

Physics 1502: Lecture 12Today’s Agenda

• Announcements:– Lectures posted on:

www.phys.uconn.edu/~rcote/– HW assignments, solutions etc.

• Homework #4:– On Masterphysics : due next Friday at 8:00 AM– Go to masteringphysics.com

• Midterm 1: next week (Oct. 5)– Covers Ch. 20-25

V R1

R2

V

R1

R2

Summary• Resistors in series

– the current is the same inboth R1 and R2

– the voltage drops add

• Resistors in parallel– the voltage drop is the same

in both R1 and R2

– the currents add

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Lecture 4

•

ε1

I1ε2

ε3

R

R

RI2

I3

RC Circuits• Consider the circuit shown:

– What will happen when we close theswitch ?

– Add the voltage drops going around thecircuit, starting at point a.

IR + Q/C – V = 0

– In this case neither I nor Q are known orconstant. But they are related,

V

a

b

c

R

C

•This is a simple, linear differential equation.

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Lecture 4

RC Circuits• Case 1: Charging

Q1 = 0, Q2 = Q and t1 = 0, t2 = tV

a

b

c

R

C

•To get Current, I = dQ/dt

Q

t t

I

RC Circuits

c

• Case 2: Discharging

• To discharge the capacitor we have totake the battery out of the circuit

a

b

R

C

•To get Current, I = dQ/dt

tIQ

t

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Lecture 4

Chapter 12, ACT 1

Consider the circuit at rightafter the switch is closed

i) What is the initial currentI?

A) 0 B) 1 A C) 2 AD) 3 A E) 4 A

I

6 Ω

6 Ω 12 µF12 V

ii) What is the current I after 2 minutes?

A) 0 B) 1 A C) 2 AD) 3 A E) 4 A

If R = 3.0 kΩ, C = 6.0 nF, ε1 = 10.0 V, Q = 18 nC,ε2 = 6.0 V, and I = 5.0 mA, what is the potentialdifference Vb –Va ?

a. –13 Vb. +28 Vc. +13 Vd. –28 Ve. +2.0V

Lecture 12, ACT 2

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Lecture 4

Electrical InstrumentsThe Ammeter

The device that measures current is called an ammeter.

Ideally, an ammeter should have zero resistance so thatthe measured current is not altered.

A

εI

R1 R2

+

-

Electrical InstrumentsThe Voltmeter

The device that measures potential difference is called a voltmeter.

An ideal voltmeter should have infinite resistance so thatno current passes through it.

V

ε

R1 R2

I Iv

I2

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Lecture 4

Problem SolutionMethod:Five Steps:

1) Focus on the Problem- draw a picture – what are we asking for?

2) Describe the physics- what physics ideas are applicable- what are the relevant variables known and unknown

3) Plan the solution- what are the relevant physics equations

4) Execute the plan- solve in terms of variables- solve in terms of numbers

5) Evaluate the answer- are the dimensions and units correct?- do the numbers make sense?

Example: Power in Resistive Electric Circuits

A circuit consists of a 12 V battery withinternal resistance of 2 Ω connected to aresistance of 10 Ω. The current in the resistoris I, and the voltage across it is V. Thevoltmeter and the ammeter can be consideredideal; that is, their resistances are infinity andzero, respectively.What is the current I and voltage V measured bythose two instruments ? What is the powerdissipated by the battery ? By the resistance ?What is the total power dissipated in the circuit ?Comment on these various powers.

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Lecture 4

Step 1: Focus on the problem• Drawing with relevant parameters

– Voltmeter can be put a two places

ε

R

I I

rA

• What is the question ?– What is I ?– What is V ?– What is Pbattery ?– What is PR ?– What is Ptotal ?– Comment on the various P’s

V

V10 Ω2 Ω

12 V

Step 2: describe the physics

• What concepts are relevant ?– Potential difference in a loop is zero– Energy is dissipated by resistance

• What are the known and unknown quantities ?– Known: R = 10 Ω ,r = 2 Ω, ε = 12 V– Unknown: I, V, P’s

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Lecture 4

Step 3: plan the solution

• What are the relevant physics equations ?

• Kirchoff’s first law:

• Power dissipated:

For a resistance

Step 4: solve with symbols• Find I: ε - Ir - IR = 0

ε

R

I I

rA

• Find V:

• Find the P’s:

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Lecture 4

Step 4: solve numerically• Putting in the numbers

Step 5: Evaluate the answers • Are units OK ?

– [ I ] = Amperes– [ V ] = Volts– [ P ] = Watts

• Do they make sense ?– the values are not too big, not too small …– total power is larger than power dissipated in R

» Normal: battery is not ideal: it dissipates energy

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Lecture 4

MagnetismThe Magnetic Force

x x x x x xx x x x x xx x x x x x

v

F

B

q

→ → → → →

→ → → → →v

F

B

q×

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑v

F = 0

B

q

Magnetism• Magnetic effects from natural magnets have been known for a

long time. Recorded observations from the Greeks more than2500 years ago.

• The word magnetism comes from the Greek word for a certaintype of stone (lodestone) containing iron oxide found inMagnesia, a district in northern Greece – or maybe it comesfrom a shepherd named Magnes who got the stuff stuck to thenails in his shoes

• Properties of lodestones: could exert forces on similar stonesand could impart this property (magnetize) to a piece of iron ittouched.

• Small sliver of lodestone suspended with a string will alwaysalign itself in a north-south direction. ie can detect themagnetic field produced by the earth itself. This is a compass.

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Lecture 4

Bar Magnet• Bar magnet ... two poles: N and S

Like poles repel; Unlike poles attract.

• Magnetic Field lines: (defined in same way as electricfield lines, direction and density)

• Does this remind you of a similar case in electrostatics?

You can see thisfield by bringinga magnet near asheet covered

with iron filings

Magnetic Field Linesof a bar magnet

Electric Field Linesof an Electric Dipole

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Lecture 4

Magnetic Monopoles• One explanation: there exists magnetic charge, just like

electric charge. An entity which carried this magneticcharge would be called a magnetic monopole (having + or -magnetic charge).

• How can you isolate this magnetic charge?Try cutting a bar magnet in half:

NS N NS S

• In fact no attempt yet has been successful in findingmagnetic monopoles in nature.

• Many searches have been made• The existence of a magnetic monopole could give an

explanation (within framework of QM) for the quantization ofelectric charge (argument of P.A.M.Dirac)

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Lecture 4

Source of Magnetic Fields?• What is the source of magnetic fields, if not magnetic

charge?• Answer: electric charge in motion!

– eg current in wire surrounding cylinder (solenoid)produces very similar field to that of bar magnet.

• Therefore, understanding source of field generated by barmagnet lies in understanding currents at atomic levelwithin bulk matter.

Orbits of electrons about nuclei

Intrinsic “spin” ofelectrons (moreimportant effect)

Forces due to Magnetic Fields?

• Electrically charged particles come under various sorts of forces.

• As we have already seen, an electric field provides a force to acharged particle, F = qE.

• Magnets exert forces on other magnets.

• Also, a magnetic field provides a force to a charged particle, butthis force is in a direction perpendicular to the direction of themagnetic field.

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Lecture 4

Definition of Magnetic FieldMagnetic field B is defined operationally by the magneticforce on a test charge.(We did this to talk about the electric field too)

• What is "magnetic force"? How is it distinguished from"electric" force?

q

F

v

mag

Start with some observations: CRT deflection• Empirical facts: a) magnitude: ∝ to velocity of q

b) direction: ⊥ to direction of q