Potentiometer

E

vref

+

R1

R2

R

µµA Vx

I

ERR

RV21

2ref +

=

I = 0 when V = Vx

Historical Potentiometer

Leeds and NorthrupK-2 Potentiometer

Galvanometer

Modern Potentiometers:Analog to Digital Converters

StaircaseGenerator

+ -

Counter

Stop

VxVref

+

Time

Vref

Vx

tstop

Vc+

Digitaloutput

Application: Electronic Thermometer

• Easy to read digital display

• Rapid response• Equilibrium

indication• Disposable

protective sheath• Inexpensive enough

for home use

Wheatstone Bridge

ER1

R2 V1

+

ERR

RV

21

21 +=

R3

R4V2

+E

RR

RV

43

42 +=

Meter voltage

ERR

R-E

RR

R

VVV

43

4

21

2

21m

++=

−=

mV

+Vm

BiopotentialsElectroencephalogram

Electro-oculogramElectroretinogram (ERG)

Electrocardiogram

Electromyogram

Impedance Pneumogram

Galvanic Skin Response

Electrical Conduction

-

-

-

-

-

-

-

-

-

+

+

+

+

+

+

++

+

+

-

-

-

-

-

-

-

Electronic Conduction

Ionic Conduction

Electrode/Electrolytic Solution Interface

Metal Electrode

C

Electrolytic Solution

Electrode/Electrolytic Solution Interface

Metal Electrode

C

Electrolytic Solution

Electrode/Electrolytic Solution Interface

Metal Electrode

C

Electrolytic Solution

Electrode/Electrolytic Solution Interface

Metal Electrode

C

Electrolytic Solution

e-

Electrode/Electrolytic Solution Interface

Metal Electrode

C

Electrolytic Solution

e-

Electrode/Electrolytic Solution Interface

Metal Electrode

C

Electrolytic Solution

e-

Electrode/Electrolytic Solution Interface

Metal Electrode

C-

Electrolytic Solution

e-

I

Electrode/Electrolytic Solution Interface

Metal Electrode

C-

Electrolytic Solution

I

Electrode/Electrolytic Solution Interface

Metal Electrode

C-

Electrolytic Solution

I

C + e- C-

Electrode/Electrolytic Solution Interface

Metal Electrode

C+

Electrolytic Solution

Electrode/Electrolytic Solution Interface

Metal Electrode

C+

Electrolytic Solution

Electrode/Electrolytic Solution Interface

Metal Electrode

C+

Electrolytic Solution

e-

Electrode/Electrolytic Solution Interface

Metal Electrode

C+

Electrolytic Solution

e-

I

C C+ + e-

Electrode/Electrolytic Solution Interface

Metal Electrode

C+

Electrolytic Solution

e-

I

C C+ + e-

Charge Build-up at Interface

+

+

+

+

+++

+

+++

++

+

++

e-

e-

e-

e-

e-

e-

e-

Charge Build-up at Interface

+

+

+

+

+++

+

+++

++

+

++

e-

e-

e-

e-

e-

e-

e-

Polarization

Equivalent Circuit+

+

+

+

+++++++

++

+

++

e-

e-e-

e-e-

e-

e-

++++++

------

Looks like a capacitor

+

+

+

+

+++++++

++

+

++

e-

e-e-

e-e-

e-

e-

++++++

------

Cp

Rp

Equivalent Circuit

But Charge “Leaks” Across the Interface

+

+

+

+

+++++++

++

+

++

e-

e-e-

e-e-

e-

e-

++++++

------

Cp

Rp

Rs

Resistance associated with charge build-up on electrode surface

Equivalent Circuit

+

+

+

+

+++++++

++

+

++

e-

e-e-

e-e-

e-

e-

++++++

------

Cp

Rp

Rs

Equivalent Circuit

Charge distribution results in a potential across the interface, the half cell potential

Ehc

Half-Cell PotentialsAl Al3+ + 3e- - 1.662 VZn Zn2+ + 2e- - 0.962 VNi Ni2+ + 2e- - 0.250 VPb Pb2+ + 2e- - 0.126 VH2 2 H+ + 2e- (Pt) - 0.0 By definitionAg + Cl- AgCl + e- + 0.223 VCu Cu+ + e- + 0.521 V2 Hg Hg2

2+ + 2e- + 0.788 VAg Ag+ + e- + 0.799 V

Half-Cell PotentialsAl Al3+ + 3e- - 1.662 VZn Zn2+ + 2e- - 0.962 VNi Ni2+ + 2e- - 0.250 VPb Pb2+ + 2e- - 0.126 VH2 2 H+ + 2e- (Pt) - 0.0 By definitionAg + Cl- AgCl + e- + 0.223 VCu Cu+ + e- + 0.521 V2 Hg Hg2

2+ + 2e- + 0.788 VAg Ag+ + e- + 0.799 V

Hydrogen Electrode

Sample Problem

A biological battery is proposed that consists of a zinc and a silver wire placed in the extracellularfluid of a biologic tissue such as muscle. What will be its output voltage. (By the way, don’t try this. Silver is toxic!) Which metal will be positive?

Muscle

V

Silver Zinc

Half-Cell PotentialsAl Al3+ + 3e- - 1.662 VZn Zn2+ + 2e- - 0.962 VNi Ni2+ + 2e- - 0.250 VPb Pb2+ + 2e- - 0.126 VH2 2 H+ + 2e- (Pt) - 0.0 By definitionAg + Cl- AgCl + e- + 0.223 VCu Cu+ + e- + 0.521 V2 Hg Hg2

2+ + 2e- + 0.788 VAg Ag+ + e- + 0.799 V

Half-Cell PotentialsAl Al3+ + 3e- - 1.662 VZn Zn2+ + 2e- - 0.962 VNi Ni2+ + 2e- - 0.250 VPb Pb2+ + 2e- - 0.126 VH2 2 H+ + 2e- (Pt) - 0.0 By definitionAg + Cl- AgCl + e- + 0.223 VCu Cu+ + e- + 0.521 V2 Hg Hg2

2+ + 2e- + 0.788 VAg Ag+ + e- + 0.799 V

Equivalent Circuit

0.799 V - 0.962 VSilver Zinc

Vm

+

Vm = 0.799 V – (- 0.962 V) = 1.761 VThe silver will be positive with respect to the zinc

Reference Electrodes