The Internal Resistance of Batteries


At this web page I've written some values of internal resistance of different batteries.
My thought is that this web page maybe helpful at the choice of power supply.

Under normal physical circumstances all electric power supplies have got some internal
resistances, Ri. The greatness Ri is used to describe how much the output voltage of a
power supply drops at a certain load. The voltage drop Vi is equal to the internal resi-
stance Ri and the load current IL. An algebraic expression:  Vi = Ri * IL

The value of Ri is mainly dependent on the ambient temperature, power dissipations of
battery and the age or charge of battery. I've drawn an equivalent diagram of a DC
power supply as follows:

Equivalent circuit diagram of a battery or another DC power supply   


Using Kirchhoff's Voltage Law
and Ohm's Law:
Please start at the negative
polarity of Vp and go clock-
wise:

0 + E - IL*Ri - Vp = 0
    <=>
E - Ri*IL = Vp
    <=>
Vp = E - Ri*IL

Please study the created formula. Vp = output voltage, E = electromotive
force and the rest is already above explained. The product Ri*IL is of
course the voltage drop Vi and the minimum value of Vp is zero. If IL = 0
=> Vp = E and you've got the unloaded output voltage.
            Back
Rip is the parallel internal resistance. This fictitious resistance describes
how fast the battery is uncharging by itself. A relatively high value of Rip
will give a longlife battery. Ri is of course also a fictitious resistance.


A procedure to determine the value of Ri

At first you solve Ri from the formula according to the following:

Vp = E - Ri*IL  <=>

Ri*IL = E - Vp  <=>

Ri = (E - Vp)/IL

See the formula above.
1. The unloaded voltage E is measured by a voltmeter.
2. A resistor with a known value RL is connected to the output.
3. The output voltage Vp is measured across the resistor.
4. IL is calculated by the formula: IL = Vp / RL
5. Ri is calculated.

At series connection you add each internal resistance of each battery cell.
Parallel coupling of battery cells is not recommended.
The values of the table below is valid at the temperature of 20 oC and
the battery must be new or fully charged.

Explainations:
IEC =  International Electrotechnical Commission.
   One L means "Alkaline Battery", e.g. LR6
 Without L means "Heavy Duty Battery", e.g. R6
 One H means "Hydride Battery", e.g. HR6
ANSI = American National Standards Institute
JIS = Japanese Industrial Standards
N = the quantity of cells
Year = the cell was bought this year
Vnom = nominal voltage
Q = charging capacity of a chargable battery
NiCd = Nickel Cadmium
NiMH = Nickel Metal Hydride
NiMH+ = Nickel Metal Hydride, second generation
Pb = lead battery cells or a car battery


Ordinary batteries or primary cells

IEC ANSI JIS N (cells) Year Vnom (Volts) E (Volts) IL (mAmps) Ri (Ohms)
LR1 N - >2 2006 1.5 1.60 10.7 0.84
R03 AAA UM4 >2 2006 1.5 1.67 21.9 1.83
LR03 AAA UM4 >2 2006 1.5 1.63 19.8 0.30
R6 AA UM3 >2 2004 1.5 1.64 104.7 0.57
LR6 AA UM3 >2 2006 1.5 1.64 107.3 0.31
R14 C UM2 >2 2006 1.5 1.66 107.1 0.49
LR14 C UM2 >2 2006 1.5 1.64 108.3 0.14
R20 D UM1 >2 2006 1.5 1.66 107.7 0.48
LR20 D UM1 >2 2006 1.5 1.65 109.1 0.13
3R12 - - 1 2006 4.5 5.01 101.7 1.97
6F22 1604D - >2 2005 9 9.93 100.9 19
6LF22 PP3 - >2 2006 9 9.78 103.0 3.98
DL2016
(CR2016)
500LC - >2 2007 3 3.25 4.5 44
DL2032
(CR2032)
5004LC - 1 2006 3 3.28 4.7 26
LR1 N - 3 2013 1.5 1.62 11.0 0.73
LR03 AAA UM4 3 2013 1.5 1.61 21.6 0.34
LR6 AA UM3 3 2013 1.5 1.62 107.5 0.28
LR14 C UM2 3 2013 1.5 1.63 107.7 0.33
LR20 D UM1 3 2013 1.5 1.63 108.4 0.25
LR23A 1181A - 1 2013 12 12.58 4.6 61
LR44 1166A - 3 2013 1.5 1.57 4.8 4.19
LR61 AAAA UM6 3 2013 1.5 1.61 10.9 0.52
3R12 - - 1 2013 4.5 5.06 105.2 1.62
3LR12 - - 1 2013 4.5 4.80 101.7 0.69
4LR61 1412A - 1 2013 6 6.28 5.2 5.74
6LF22 PP3 - 3 2013 9 9.71 19.9 18
CR2032 5004LC - 3 2013 3 3.38 5.8 29


Rechargeable batteries or secondary cells

Type or
IEC
N (cells) Year Q (mAh) Vnom (Volts) E (Volts) IL (mAmps) Ri (mOhms)
NiCd 1 2006 850 1.2 1.26 102 300
NiCd 1 1990s 500 3.6 3.9 50 4000
NiMH 1 2005 2200 1.2 1.38 112 270
NiMH 1 2005 2000 1.25 1.39 114 220
Pb 1 2005 1300 6 6.22 111 270
Pb 1 2004 12000 6 6.30 1200 70
HR03 2 2013 1000 1.2 1.36 112.1 300
HR6 4 2013 2600 1.2 1.39 114.8 300
HR03+ 4 2013 800 1.2 1.45 101.4 340
HR6+ 2 2013 2000 1.2 1.44 100.4 300
HR14+ 1 2013 4500 1.2 1.40 391.0 230
HR20+ 1 2013 8500 1.2 1.39 751.9 230
6HF22+ 1 2013 200 9 9.86 21.0 3300


Calculation of data concerning Ri

Calculations




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