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