Test of the Batteries for the Sweeping Current Source
  -------------------------------------------------------


                                  Original Rev.  14-June-2022
                                   Current Rev.   8-July-2022


This file is notes about testing the batteries that are
used in the operation of the Sweeping Current Source.
These batteries are  Power Sonic  model PS-12350.

These batteries are rated for  35 Amp-Hours  at a 20 hour
rate  or for  33 Amp-Hours  at a 10 hour rate.  This is
with a discharge termination voltage of  10.8 Volts.

Other important characteristics are:

   Design Lifetime  5 years

   Internal Resistance  about  12 mill Ohms

   Allowed Maximum Discharge Rate for 5 seconds  495 Amps

   Self Discharge about  73%  of normal capacity
   after 6 months when stored at room temperature

   Floating Charge Voltage  13.5 to 13.8 Volts
   for 6 cells at 20 deg C


With a 15 Ohm load, battery #1  fell to  10.8 Volts  in
about 23.1 hours.  The average voltage was about 12.4 Volts
so the average current was about  825 mA.  Doing just a
multiplication instead of an integration this gives an
energy storage capacity of about    19 Amp-Hours    for
Battery #1.   At the beginning of the discharge curve for
Battery #1  you can see when the DVM + load was connected.


With a 15 Ohm load, battery #2  fell to  10.8 Volts  in
about 31 hours.  The average voltage was about 12.4 Volts
so the average current was about  825 mA.  Doing just a
multiplication instead of an integration this gives an
energy storage capacity of about    25.6 Amp-Hours    for
Battery #2.  When the test of Battery #2 started the charger
was left on it for the first 6 measurements and then I let
the battery just float through measurement 13 and then
connected the load during measurement 14.


Both discharge curves were make with 10 measurements
per hour.  Each measurement was 10 readings of the DVM
spaced 1 second apart and checked for RMS noise and slope.


Note that Power Sonic's  35 Amp-Hour  rating of this
battery is based on a 20 hour discharge period down to
a cut-off voltage of 10.8 Volts.  This is an average
discharge current of  1.75 Amps.   The Sweeping Current
Source draws less than this.

If these batteries were in good condition then our test
with a lower discharge current  ( 825 mA)  would have
resulted in a  higher  Amp-Hour rating than the 35 Amp-Hours
obtained in the Power Sonic specification using a 1.75 Amp
discharge.


Safety Calculation:
-------------------

A normal things to have in the area of the SQUID based
JJ test setup would be a 1 foot length of AWG #20 wire.
How safe is this ?

1 foot of AWG #20 wire has about  12 mOhm  of resistance.

1 foot of AWG #20 weighs about  1.40 grams

heat capacity of copper   0.385  Joules / gram deg C

heat capacity of 1 foot of AWG #20 copper wire is about
0.54 Joules per deg C

If this 1 foot of #20 wire is put across the battery
terminals then about 500 Amps will flow through it.

12 mOhm in the wire  plus  12 mOhm internal to the battery.

12 Volts divided by 24 mohms gives 500 Amps.

500 Amps times 6 Volts gives 3000 Watts.

Thus we will put about 3000 Watts into the 1 ft of wire
or about 3000 Jouls per second.

The wire temperature will rise by  5555 deg C in one second

Copper melts at 1085 deg C

The copper wire will melt in under 200 msec,  i.e. faster
than you can let go of it.