When three different resistors are connected in series to a battery, the total resistance is the simple sum of the individual components, which directly dictates your current draw, heat dissipation, and required battery capacity. For power system builders, wiring multiple power resistors in series is the standard method for creating a high-wattage DC dummy load bank to capacity-test a battery without exceeding the wattage rating of a single resistor.
This guide walks through the exact circuit math, battery sizing with Peukert and efficiency derating, and the charge/discharge limits required to safely run this test rig.
The Scenario: Sizing a Battery for a Series Resistor Load Bank
Before we calculate runtime, we need to define the system block from source to load. A proper DC test circuit requires more than just wires and resistors; it requires protection and switching.
- Source: 12V Nominal (12.8V resting) LiFePO4 Battery Bank.
- Protection: Class T fuse or ANL fuse sized 125% above max continuous current, placed within 7 inches of the battery positive terminal.
- Switching: Heavy-duty DC contactor or marine battery disconnect switch rated for the calculated amperage.
- Load: Three different chassis-mount power resistors wired in series.
By using three different resistor values in series, you can fine-tune the total resistance to hit a specific target current while distributing the thermal load across multiple heatsinks. According to All About Circuits, in a series circuit, the current is identical through every component, but the voltage drop and power dissipation scale proportionally with each resistor's value.
Circuit Math: Current, Voltage, and Power Dissipation
Let's assign real-world values to our three resistors to build a 150W+ dummy load. We will use aluminum-housed chassis mount resistors:
- R1: 0.2Ω
- R2: 0.3Ω
- R3: 0.5Ω
Total Resistance (Rt): 0.2 + 0.3 + 0.5 = 1.0Ω
Assuming a fully charged LiFePO4 battery resting at 13.2V (dropping to a nominal 12.8V under load), we use Ohm's Law (I = V / R) to find the current:
- Initial Current: 13.2V / 1.0Ω = 13.2A
- Nominal Current: 12.8V / 1.0Ω = 12.8A
Because the current is constant in a series circuit, we must calculate the power dissipation (P = I² × R) for each individual resistor to ensure we buy the correct physical wattage rating. Using the nominal 12.8A draw:
| Component | Resistance | Voltage Drop | Power Dissipated | Minimum Required Resistor Rating |
|---|---|---|---|---|
| R1 | 0.2Ω | 2.56V | 32.7W | 50W Chassis Mount |
| R2 | 0.3Ω | 3.84V | 49.1W | 75W Chassis Mount |
| R3 | 0.5Ω | 6.40V | 81.9W | 100W Chassis Mount |
| Total | 1.0Ω | 12.80V | 163.7W | N/A |
Battery Sizing: Peukert, DoD, and C-Rate Limits
Now that we know our continuous load is 12.8A, we can size the battery. Suppose we want to run this load bank for a 5-hour capacity test.
Base Math: 12.8A × 5 hours = 64Ah.
However, you cannot size a battery on base math alone. We must apply Depth of Discharge (DoD) limits, C-rate constraints, and efficiency factors.
- Depth of Discharge (DoD): LiFePO4 cells can technically handle 100% DoD, but to achieve a 4,000+ cycle life, you should limit discharge to 80%. Adjusted Capacity: 64Ah / 0.80 = 80Ah.
- Peukert's Law & Efficiency: Peukert's exponent describes how a battery's effective capacity drops at higher discharge rates. While lead-acid batteries suffer heavily from this (exponent ~1.3), LiFePO4 chemistry is highly efficient (exponent ~1.05). However, system wiring resistance, BMS FET voltage drops, and connection losses introduce a real-world efficiency factor of about 95%. Adjusted Capacity: 80Ah / 0.95 = 84.2Ah.
- C-Rate Check: A 12.8A draw on an 85Ah battery is roughly a 0.15C discharge rate. LiFePO4 cells comfortably handle continuous discharge rates up to 1C, so thermal runaway from high-current stress is not a factor here.
Based on this math, the minimum viable battery is an 85Ah unit. The next standard commercial size up is 100Ah.
Series vs. Parallel Battery Configurations for this Load
What happens if you decide to add a second 12V 100Ah battery to your test rig? The consequences for voltage (V) and amp-hours (Ah) depend entirely on how you wire them, and this drastically changes your 1.0Ω resistor load behavior.
| Configuration | Resulting V & Ah | Impact on 1.0Ω Series Load | Verdict |
|---|---|---|---|
| Series | 24V / 100Ah | Current doubles to 25.6A. Total power jumps to 655W. Your 100W resistor (R3) will instantly overheat and fail. | Reject. Requires redesigning the resistor bank for 24V. |
| Parallel | 12V / 200Ah | Current remains 12.8A. Power remains 163.7W. Runtime doubles from 5 hours to 10 hours. | Accept. Ideal for extended endurance testing. |
Critical Rule for Parallel Wiring: Never parallel mismatched cells, different capacities, or batteries of different ages. When paralleling two 12V LiFePO4 batteries, they must be the exact same model, purchased at the same time, and topped to the exact same voltage (within 0.05V) before connecting them together. If you parallel a 100Ah battery with a 50Ah battery, the larger battery will force high equalization currents into the smaller one, potentially tripping the smaller battery's BMS or melting its internal busbars.
Inverter and Charger Sizing for the Test Rig
Even though the three resistors are connected in series directly to the battery as a DC load, a complete test rig requires a charging solution and often an inverter to run AC auxiliary equipment (like a cooling fan for the resistor bank or an AC-powered datalogger).
Charger Sizing:
The maximum recommended charge rate for standard cylindrical or prismatic LiFePO4 cells is 0.5C, but 0.2C is the sweet spot for longevity and avoiding BMS overheating. For a 100Ah battery, 0.2C equals 20A.
Selection: You need a 14.6V LiFePO4-specific smart charger rated for at least 20A. (Do not use a standard lead-acid AGM charger; the equalization phase will push 15V+ and trigger the BMS over-voltage protection).
Inverter Sizing:
Assume you need to run a 120V AC box fan (40W) to cool the resistors and a laptop datalogger (60W). Total AC load = 100W.
Selection: Inverters operate most efficiently between 30% and 50% of their rated load. A 300W Pure Sine Wave inverter is the correct pick here. It will draw roughly 9A from the 12V battery to power the 100W AC load, which must be added to your 12.8A DC resistor load for a total system draw of 21.8A during the test.
Decision Tree: Selecting the Exact Battery and BMS
To finalize the build, follow this decision path to select the exact power source for your series resistor load bank.
- IF your total calculated continuous current (Resistors + Inverter) is under 50A AND you need a drop-in replacement for an AGM footprint...
THEN choose a 12V 100Ah Group 24/27 LiFePO4 battery with an internal 100A BMS. - IF your load exceeds 100A (e.g., you changed R3 to 0.05Ω to test high-current voltage sag)...
THEN you must step up to a 200Ah battery with a 200A BMS, or parallel two 100Ah batteries (matching rules apply). - IF you are building a raw DIY cell pack (4S configuration) for this test...
THEN you must select an external BMS rated for 120% of your max load, such as the JBD Smart BMS 120A.
The Default Recommendation:
For the 12.8A continuous load established in this guide, the most reliable, cost-effective, and safe choice is the Ampere Time 12V 100Ah LiFePO4 Deep Cycle Battery. It features a built-in 100A BMS, easily handles the 0.15C discharge rate without voltage sag, and fits standard marine/RV battery boxes. Pair it with a Victron Energy Blue Smart IP22 12V 20A Charger to ensure the charging profile perfectly matches the LiFePO4 absorption curves without risking over-voltage faults.
By calculating the exact power dissipation of your series resistors and applying strict DoD and efficiency derating to your battery math, you ensure your test rig provides accurate capacity data without melting your bench or damaging your cells.
