Today: dc circuits mostly current & resistance.

today: dc circuits

mostly current & resistance

not so funny now.

just wait ...

battery = pumpvoltage = pressure

current = flowresistor = constriction

capacitor = diaphragm / flexible reservoirdiode = check valve

inductor = paddle wheel

real V source = ideal V source + R

actual circuit has a parasitic r

R in series with output(“steals” V)

real current sources

R in parallel with output(“steals” I)

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

series resistors: conservation of energy

-+

R2

I I

∆V

R1a cbReq

∆V

a c

-+


voltage divider

R2

R1Vin Vout

Vout = R2

R1+R2Vin

signal in signal

out

R1

R2

volume


parallel resistors: conservation of charge

current divider

I

-+

R1

∆V

R2

a bI1

I2

∆V1=∆V2=∆V

-+

Req

∆V

Req R1 R2

1 11 = +

rank the currents


more complex arrangements

measuring voltage

real voltmeters

measuring current

a simple ammeter


dc Circuits, part II

same thing, just more of it


Thévenin equivalents

any combination of R’s and V’sis equivalent to a SINGLE R and V

(Norton equivalent: a single I source in parallel with R)

Vth = V (open circuit)

Rth = V (open circuit)

I (closed circuit)

disconnect from red dots = open circuit voltageshort red dots, current there is closed-circuit current.

This image: Horowitz & Hill, The art of electronics


series resistors: conservation of energy

-+

R2

I I

∆V

R1a cbReq

∆V

a c

-+

source voltage = sum of voltages on resistors


parallel resistors: conservation of charge

current divider

I

-+

R1

∆V

R2

a bI1

I2

∆V1=∆V2=∆V

-+

Req

∆V

Req R1 R2

1 11 = +

source current = sum of currents in resistors


so what?

V

R

real sources = ideal sources + R

real meter = ideal meter with

R

VI R

what about ammeter?


V source loading

V

r

source

extra seriesresistance

Rload

∆Vload = V - Ir

for r ≪ Rload, ∆Vload ≈ V

V source wants R high

one solution:large resistor in parallel with load

I


Ip

I source loading

source

extra parallelresistance

Rload

I source wants R lowsourcing currents at high Rload is hard

Ir

Iload

Iload = Ir

r+R

for Rload ≪ r, Iload ≈ I


measuring the meter

Rload

I

Vr

realmeter

Req

I

V

idealmeter

∆Vload = IReq = R1+R/rI Rload ≪ r, ∆Vload ≈ IR


summaryvoltmeter wants R low!can use a buffer/follower ... later

I source wants R lowtransformer pre-ampconsider sourcing V

V source wants R highlarge series + parallel resistorspresent large R


Sourcing current

Rwires

Rwires

RthingI V

This is what a hand meter does.

Why is it no good?

Vmeter = I(Rthing + 2Rwires)


Sourcing current, properly

No problem.You just need four wires.

Rwires

Rwires

Rthin

g

I V

Rthing ≪ Rinternal

or add buffer


Sourcing voltage

Rwires

Rwires

RthingVs

Still have to measure voltage on devicethe wires still use up some of V

What about current?

V


Sourcing voltage better

R = ∆V / I

Note we need 4 wires againcurrent meter - not hardstill problems?

Rwires

Rwires

Rthing

Vs

V

ΙΙ

=Rprecise

V

Rs


source/meter resistances

voltmeter wants R lowbut V source wants R high

need buffer/amp on V meter resistor in parallel with source

if V source is problem, R is too lowconsider sourcing I


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

Rwires

Rwires

Rthing

Vs V

Ι

=Rs ≪ Rthing

Rp

Ι

=

V

source voltageRp has same voltage as Rthing

Rs has same current

have done >1010 Ohm


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

Rwires

Rwires

Rthin

g

I V

this works just fine ...so long as your V meter is good or you can tolerate large Iv. good amp / part of a bridge


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

V

R1 R3

R2 Rx+dR

Vs

balance bridge to V=0detect small changes from null

make R1-R3 about the sametrimming resistor on R2 = dR

R2 =

≈ R3


Rules for analyzingmore complicated

circuits


+

+

+


capacitors

frequency-dependent resistorI and V are 90o out of phasecan’t dissipate power, ideally


combinations of capacitors


capacitors with stuff inside

Q0

+-

C0

∆V0

Q0

+-

Dielectric

C0

∆V


rc circuits

R

C

S

V ∝ e-τ/RC

VE


RC differentiatorC

Vin (t) Vout (t)R

for small RC, }


RC integrator

CVin (t) Vout (t)

R

for large RC (V ≪ Vin)}


so what?

filtering of signals

unintentional capacitive couplingsee from waveform shape

more later


ac resistive circuits

nothing earth-shattering happens

except P is lower than you expect


ac capacitive circuitsI and V 90o out of phaseaverage power is ZERO

frequency response?insulating at dcconducting at high f

voltage “lags” current


filters

C

RVin Vout

low-pass

CVin Vout

R

high-pass


familiar?

low-pass filter

C

RVin Vout

CVin Vout

R

high-pass filter

differentiatorintegrator

frequency domain⇕

time domain

audio crossovers

dB/decade ...

+-

+Vcc

-Vcc

100k

photo-diode

+Vcc

741

741 pinout

output

Today:amplify photodiode signal

Today: dc circuits mostly current & resistance.

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