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WARNING:Exam is Thursday, 7:30 – 9 pm

Room 54-100Review Sessions:

Me: Tuesday 4-6 pm 6-120

Imran: Wednesday 8-10 pm 4-270

In class: Thursday 12-2 pm; 2-4 pm

Office Hours:

Brian F.: Tuesday 8-10 pm 6-402

Brian P.: Wednesday 4-6 pm 6-106

Please email me questions

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Class 12: Outline

Hour 1:

DC Circuits

Hour 2:

Expt. 6: Simple Circuits

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Last Time:Capacitors & Dielectrics

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Capacitors & Dielectrics

QC

V

To calculate:

1) Put on arbitrary ±Q

2) Calculate E

3) Calculate V

22

2

1

2

1

2VCVQ

C

QU

23 3

2o

E

Eu d r d r

0S inqd AE

Dielectrics

Filled with Dielectric 0C C

Energy

Capacitance

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This Time:DC Circuits

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Examples of Circuits

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Current: Flow Of Charge

Units of Current: Coulombs/second = Ampere

Average current Iav: Charge Q flowing across area A in time t av

QI

t

Instantaneous current: differential limit of Iav

dQI

dt

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Direction of The CurrentDirection of current is direction of flow of pos. charge

or, opposite direction of flow of negative charge

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Current Density J

ˆS S

I dA d J n J A

J: current/unit area

points in direction of current

IJ ˆA

I

I

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Why Does Current Flow?

If an electric field is set up in a conductor, charge will move (making a current in direction of E)

Note that when current is flowing, the conductor is not an equipotential surface (and Einside ≠ 0)!

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Microscopic Picture

Drift speed is velocity forced by applied electric field in the presence of collisions.

It is typically 4x10-5 m/sec, or 0.04 mm/second!

To go one meter at this speed takes about 10 hours!

How Can This Be?

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Conductivity and Resistivity

: conductivity

: resistivity

Ability of current to flow depends on density of charges & rate of scattering

Two quantities summarize this:

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Microscopic Ohm’s Law

or E J J E

and depend only on the microscopic properties of the material, not on its shape

1

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Demonstrations:Temperature Effects on

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PRS Questions:Resistance?

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Why Does Current Flow?Instead of thinking of Electric Field, think of potential difference across the conductor

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Ohm’s Law

What is relationship between V and current?b

b a aV V V d E E s

/E VJ

V I IRAI

JA

/E VJ

IJ

A

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Ohm’s Law

RA

IRV R has units of Ohms () = Volts/Amp

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Examples of Circuits

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Wires in CircuitsWires in circuit diagrams are “perfect conductors.” They are thus equipotentials, and can be stretched, shrunk... as long as you don’t change the potentials!

Must maintain all equipotential

surfaces!

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Symbols for Circuit Elements

Battery

Resistor

Capacitor

Switch

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Sign Conventions - Battery

Moving from the negative to positive terminal of a battery increases your potential

b aV V V

Think:

Ski Lift

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Sign Conventions - Resistor

Moving across a resistor in the direction of current decreases your potential

b aV V V

Think:

Ski Slope

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Sign Conventions - Capacitor

Moving across a capacitor from the negatively to positively charged plate increases your potential

b aV V V

Think:

Ski Lodge

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Series vs. Parallel

Series Parallel

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Resistors In SeriesThe same current I must flow through both resistors

1 2V I R I R

1 2eqR R R 1 2( ) eqI R R I R

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Resistors In ParallelVoltage drop across the resistors must be the same

1 2 1 1 2 2 eqV V V I R I R IR

1 2I I I

1 2

1 1 1

eqR R R

1 2 eq

V V V

R R R

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Measuring Voltage & Current

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Measuring Potential Difference

A voltmeter must be hooked in parallel across the element you want to measure the potential difference across

Voltmeters have a very large resistance, so that they don’t affect the circuit too much

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Measuring Current

An ammeter must be hooked in series with the element you want to measure the current through

Ammeters have a very low resistance, so that they don’t affect the circuit too much

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Measuring Resistance

An ohmmeter must be hooked in parallel across the element you want to measure the resistance of

Here we are measuring R1

Ohmmeters apply a voltage and measure the current that flows. They typically won’t work if the resistor is powered (connected to a battery)

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Experiment 6:Simple Circuits

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PRS Questions:Light Bulbs

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Kirchhoff’s Loop Rules

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Kirchhoff’s Rules1. Sum of currents entering any junction in a circuit

must equal sum of currents leaving that junction.

1 2 3I I I

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Kirchhoff’s Rules2. Sum of potential differences across all elements

around any closed circuit loop must be zero.

PathClosed

dV 0sE

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Internal Resistance

Real batteries have an internal resistance, r, which is small but non-zero

b aV V V I r Terminal voltage:

(Even if you short the leads you don’t get infinite current)

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Steps of Solving Circuit Problem

1. Straighten out circuit (make squares)

2. Simplify resistors in series/parallel

3. Assign current loops (arbitrary)

4. Write loop equations (1 per loop)

5. Solve

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Example: Simple CircuitYou can simplify resistors in series (but don’t need to)

What is current through the bottom battery?

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Example: Simple CircuitStart at a in both loops

Walk in direction of current

1 1 22 0I R I I R

2 1 0I I R

Add these: 12 0I R 1I R

We wanted I2: 2 1I I R 2 1I IR

2 0I

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Group Problem: Circuit

HARDER EASIER

Find meters’ values. All resistors are R, batteries are