The Internal Resistance of Batteries |
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At this web page I've written some values of internal resistance of different batteries. |
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:
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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 |
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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. |
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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. |
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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 |
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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