Page 58 - Battery Reference Book

Calculation of energy density of cells 1/43
Table 1.17 Effect of internal, external and total electrical resistance on available current from a 48 two-volt (6) cell battery (8V)
comprising 12 strings of four cells in series
~~ ~
mln 0.333 0.333 0.333
ReXt (total for battery) (Q) 0.1 0.5 2
r T P
R,, internal resistance/cell (Q) 0.1 0.2 0.1 0.2 0.5 0.2 0.5
RTOT = (m1n)Rc + Rext 0.1333 0.1666 0.5333 0.5666 0.6665 2.0666 2.1665
IIRTOT 7.50 6.00 1.87 1.76 1.50 0.484 0.461
ETOT = mE, 8 8 8 8 8 8 8
60 48 15 14.1 12 3.87 3.69

114.8 91.8 28.7 26.9 22.9 7.40 6.87
480 384 120 112.8 96 31.0 29.5
m x h x ETOT
960
Capacity, ~- 768 240 225 192 61.9 59.0
(A h)
RTOT
Table 1.18 Effect of internal, external and total electrical resistance on available current from a 48 two-volt (Ec) battery (24V) comprising
four strings of twelve cells in series
mln 3.000 3.000 3.000
Re,, (total for battery) (Q) 0.1 0.5 2
, A P
0.1 0.2 0.1 0.2 0.5 0.2 0.5
0.400 0.700 0.800 1.100 2.000 3.600 4.500
2.50 1.42 1.25 0.909 0.500 0.277 0.222
24 24 24 24 24 24 24
60 34.3 30 21.8 12.0 6.7 5.3

344.4 197.0 172.2 125.0 68.9 38.7 30.2
1440 823 720 523 288 160.8 127.2
~~ETOT
Capacity, __- (Ah) 2880 1646 1440 1046 576 321 254
&or

29% by weight to a final concentration of 21% by 24 V battery 8 V battery
weight, 53.9 Ah are produced when the cell temper- 7Or 4 strings of 12 cells 12 strings of 4 cells
(m = 4. n = 12)
(m=l~,n=4)
ature is 25T, i.e. capacity = 53.9Ah at a voltage of
about 2V. Thus 107.8 Wh are produced. The weights
in grams of active materials involved are as follows:
Lead 207.2
Lead dioxide 223.2
Sulphuric acid 196.0
=TOT 0 ~ RTOT - ‘TOT
Total active matlerial 626.4 g Slope of line = ETor
Thus the gravimetric energy density in W hkg of
active material is:
107.8 x lOOQ
626.4 =: 172 (or 250.5 if electrolyte is excluded) Reciprocal electrical resistance. llRTo,
This can be considered to be the maximum theoreti-
cal energy density of the lead-acid battery. In practice, Figure 1.20 Plot of reciprocal of total electrical resistance l/R~or
versus current, /Tor