Copper Sulfate Resistors

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Definition:                           

Equation

Parameters

Diagram

Calculate Properties of Solution:              top

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Parameter

Value

Units

Special Values

Inputs:

D (diameter)
l (length)
R (resistance)  
 

Outputs:  

C's (conc. solute)

C'w (conc. water)

C's (alternate)

V (volume)

  ρ (resistivity)

A (area)

Output Format:                                                        top

Select Format: Scientific Engineering Fixed

 

Notes:                                                                       top

bulletThe alternate value for C'S is obtained from a fit to measured data found here.  This is a fit to measured data that covers much higher resistivities.  The equation is log(C's)=(log(1553)-log(ρ))/0.7465, where C'S is in g/l and ρ is in Ohm-cm.
bulletYou should use de-ionized water and copper electrodes to reduce resistance change over time.
bulletExample:  Suppose you want to make a 1000 ohm resistor out of 1" inner-diameter Tygon tubing with copper electrodes inserted at each end with 1 foot between electrodes.  The calculator gives C's=19.653 g/l and C'w= 991.41 g/l.  So, to make one liter of solution, fill a jar with 991.41 g of water and 19.653 g of CuSO4*5H2O (or make a smaller batch keeping the same proportions).  Note:  you could just add the amount, C's, to one liter of water with negligible error (you have to do this for the alternate version of C's).  Also, if you want to make just enough then use the volume (in liters) from the calculator and multiply this by C's to get the amount of CuSO4*5H2O you need, then fill with water.
bulletCuSO4*5H2O is know by several names (copper sulfate, cupric sulfate, cupric sulfate pentahydrate,...) and appears as blue crystals.
bulletCalculator assumes solution temperature of 20oC (68oF).  Actual resistance is a function of water temperature.
bulletIn the table below, the left three columns are data from the CRC Handbook of Chemistry and Physics.  H% is the percent of hydrate (CuSO4*5H2O) by weight in the solution.  D204 is the relative density of the solution at 20oC compared to water at 4oC.  γ is the specific conductance at 20oC.  The right three columns are derived from the others for this calculator.
bullet

H%

[by wt.]

D204

g

[mS/cm]

Cs'

[g/l]

CW'

[g/l]

r

[W-m]

1.56

1.0085

5.4

15.7

992.8

1.852

3.13

1.0190

9.3

31.9

987.1

1.075

4.69

1.0296

12.8

48.3

981.3

0.781

6.26

1.0403

16.0

65.1

975.2

0.625

7.82

1.0511

19.0

82.2

968.9

0.526

9.39

1.0620

21.9

99.7

962.3

0.457

10.95

1.0730

24.6

117.5

955.5

0.407

12.52

1.0842

27.2

135.7

948.5

0.368

14.08

1.0955

29.7

154.2

941.3

0.337

15.64

1.1070

32.2

173.1

933.9

0.311

17.21

1.1186

34.4

192.5

926.1

0.291

18.77

1.1304

36.6

212.2

918.2

0.273

20.34

1.1424

38.6

232.4

910.0

0.259

21.90

1.1545

40.5

252.8

901.7

0.247

23.47

1.1669

42.3

273.9

893.0

0.236

25.03

1.1796

44.0

295.3

884.3

0.227

26.59

1.1926

45.6

317.1

875.5

0.219

28.16

1.2059

47.0

339.6

866.3

0.213

bulletNote that CRC Handbook gives values for Cs and Cw, but these count the 5H2O as part of the solution, not the solute, which would result in a slight error if not accounted for (this is why my values have the prime symbol).
bulletDensity of 20oC water is actually 0.99823 [g/ml] from this table.
bulletIf you want to use anhydrous CuSO4 (gray powder) then multiply amount of solute by 0.639 (you need less) and use more water given by the difference.

 

 

 

 

Copyright 2003  Raymond J. Allen