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The Plan. dielectrics, quickly current & resistance HW3 hints after the break (& in lab) time permitting, some of dc circuits. Exam 1. Right here, 3pm Thursday electric forces & fields electrical potential & energy current & resistance NO RELATIVITY study quick quizzes, example probs

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The Plan

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The Plan

  • dielectrics, quickly

  • current & resistance

  • HW3 hints after the break (& in lab)

  • time permitting, some of dc circuits


Exam 1

  • Right here, 3pm Thursday

    • electric forces & fields

    • electrical potential & energy

    • current & resistance

    • NO RELATIVITY

  • study quick quizzes, example probs

  • our HW and quizzes

  • problems in notes

relax.

it will be ok.


not so funny now.


battery = pump

voltage = pressure

current = flow

resistor = constriction

capacitor = diaphragm / flexible reservoir

diode = check valve

inductor = paddle wheel


with the time left ...

let’s get a jump on dc circuits


real battery = ideal battery + R


actual circuit has a parasitic r


real current sources


series resistors: conservation of energy

Req

R1

R2

a

b

c

a

c

I

I

-

+

-

+

∆V

∆V

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


R2

voltage divider

Vout =

Vin

R1+R2

R1

signal

in

Vin

Vout

R1

signal

out

R2

volume

R2

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


1

1

1

parallel resistors: conservation of charge

=

+

Req R1 R2

∆V1=∆V2=∆V

R2

Req

I1

R1

a

b

I2

I

-

+

-

+

∆V

∆V

current divider

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


more complex arrangements

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


measuring voltage


real voltmeters


measuring current


a simple ammeter


V (open circuit)

Thévenin equivalents

Rth =

I (closed circuit)

Vth = V (open circuit)

any weird combinations of R’s and V’s

is equivalent

to a

SINGLE R and V

(or a single I source

in parallel with R)

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


so what?

V

E

I

R

R

real sources =

ideal sources + R

real meter =

ideal meter with R

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


V source loading

∆Vload = V - Ir

for r ≪ Rload,

∆Vload ≈ V

V

Rload

r

I

V source wants R high

one easy solution:

large resistor in parallel with load

source

like a battery

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


r

Iload = I

r+R

I source loading

Rload

r

for Rload≪r,

Iload ≈ I

I

Ip

Iload

source

I source wants R low

sourcing currents at high Rload is hard

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


R

I

I

measuring the meter

V

1+R/r

r

Rload

Req

V

real

meter

ideal

meter

∆Vload = IReq =

Rload≪r, ∆Vload ≈ IR

I

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


summary

voltmeter wants R low!

can use a buffer/follower

I source wants R low

transformer pre-amp

consider sourcing V

V source wants R high

large series + parallel resistors

present large R

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


Sourcing current

This is what a hand meter does.

Why is it no good?

Rwires

I

V

Rthing

Rwires

Vmeter = I(Rthing + 2Rwires)

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


Sourcing current, properly

Rwires

V

I

Rthing

Rthing≪ Rinternal

or add buffer

Rwires

No problem.

You just need four wires.

What is still wrong?

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


Sourcing voltage

Rwires

V

Rthing

Vs

Rwires

Still have to measure voltage on device

the wires still use up some of V

What about current?

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


Sourcing voltage II

V

Rwires

Vs

Rthing

Rs

Rpar

Ι

Ι

Rwires

=

R = ∆V / I

Note we need 4 wires again

current meter - not hard

still problems?

Rprecise

V

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


source/meter resistances

voltmeter wants R low

but V source wants R high

need buffer/amp on V meter

resistor in parallel with source

if V source is problem, R is too low

consider sourcing I

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


what if I want to measure a *really* high R?

V

Ι

Rwires

Vs

Rthing

Rp

Ι

Rwires

=

=

source voltage

Rp has same voltage as Rthing

Rs has same current

have done >1010 Ohm

Rs≪ Rthing

V

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


what if I want to measure a *really* low R?

Rwires

V

I

Rthing

Rwires

this works just fine ...

so long as your V meter is good

v. good amp / part of a bridge

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


what if I want to measure a small change in R?

R2 =

R1

R3

≈ R3

V

Vs

R2

Rx+dR

balance bridge to V=0

detect small changes from null

make R1-R3 about the same

trimming resistor on R2 = dR

THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


THE UNIVERSITY OF ALABAMA

CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY

An NSF Science and Engineering Center


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