The Physics of Charge: From Coulombs to Amp-Hours
At the most fundamental level, an electrical charge is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electrons carry a negative charge, while protons carry a positive charge. The standard SI unit for this property is the Coulomb (C), where one Coulomb equals approximately 6.242 × 10^18 electrons. For deep technical reference on SI base units, the NIST SI Units guide provides the exact metrological definitions.
But on the workbench, we rarely count Coulombs. We measure the flow of charge over time. One Ampere is defined as one Coulomb of charge moving past a point in one second. Therefore, 1 Amp-hour (Ah) equals exactly 3,600 Coulombs. When you buy a '100Ah battery', you are buying a reservoir capable of delivering 360,000 Coulombs of electrical charge.
In any DC power system, charge flows in a continuous loop. The Source (battery) uses chemical potential to separate charge, creating voltage (electrical pressure). The Conductors (copper busbars and wires) provide a low-resistance path for the charge to flow as current. The Load (inverter) forces the moving charge through high-frequency MOSFETs, converting the DC charge flow into an AC waveform to run household appliances.
Series vs. Parallel: Manipulating Voltage and Charge Capacity
When building a battery bank, you wire cells together to achieve the voltage and Amp-hour capacity your inverter requires. The physics of charge dictates strict rules for how these configurations behave.
| Configuration | Voltage Consequence | Charge Capacity (Ah) | Total Energy (Wh) | Primary Use Case |
|---|---|---|---|---|
| Series (4x 12V 100Ah) | Adds (48V) | Stays Same (100Ah) | 4,800Wh | High-power systems (>3000W) to keep DC current low. |
| Parallel (4x 12V 100Ah) | Stays Same (12V) | Adds (400Ah) | 4,800Wh | 12V DC loads, RVs, marine, low-power off-grid cabins. |
In a series circuit, the same electrical charge must push through every battery sequentially. The voltage (potential difference) stacks, but the Ah capacity remains limited by a single battery. In a parallel circuit, the voltage remains constant, but the total charge capacity adds up because the current divides among the branches.
Never parallel mismatched cells, different chemistries, or batteries of vastly different ages. If a 12.8V LiFePO4 battery is paralleled with a degraded 12.2V unit, the higher-voltage battery will violently dump charge into the lower-voltage battery to equalize. This uncontrolled cross-current bypasses the Battery Management System (BMS) charge limits, leading to cell venting, thermal runaway, and catastrophic lithium fires. Always parallel identical models purchased at the same time, and use busbars for symmetrical wiring.
Sizing Math: Peukert’s Law, C-Rates, and Depth of Discharge
A battery's stated Ah rating is a theoretical maximum based on a very slow discharge. In reality, the usable electrical charge is governed by chemistry, defined by Peukert's Law, C-rates, and Depth of Discharge (DoD).
C-Rate defines the speed of charge/discharge relative to capacity. A 1C rate on a 100Ah battery means drawing 100A (empty in 1 hour). A 0.5C rate means drawing 50A (empty in 2 hours).
Peukert’s Law calculates actual capacity under load: t = H × (C / (I × H))^k. The exponent k represents internal losses. Flooded Lead-Acid (FLA) batteries have a k of ~1.3. Lithium Iron Phosphate (LiFePO4) has a k of ~1.05. For detailed C-rate and Peukert discharge curves, refer to the Battery University C-Rate guide.
Worked Example: You have a 100Ah FLA battery rated at the 20-hour mark (5A draw). You connect a 50A load (C/2). Because of Peukert's effect (k=1.3), you do not get 2 hours of runtime. You get roughly 1.1 hours (55 usable Ah). If you swap to a 100Ah LiFePO4 battery (k=1.05), that same 50A load yields 1.8 hours (90 usable Ah).
Depth of Discharge (DoD) Limits:
- FLA/AGM: Limit to 50% DoD to prevent sulfation. A 100Ah battery yields 50 usable Ah.
- LiFePO4: Safely discharge to 80-90% DoD. A 100Ah battery yields 80-90 usable Ah.
Inverter and Charger Sizing for the Stated Load
To move electrical charge from the battery to your appliances efficiently, your inverter and charger must be sized to handle the continuous current, surge demands, and chemical charge limits of the battery.
The Scenario: You need to run a 1200W microwave and a 300W fridge simultaneously on a 12V system. Total continuous load = 1500W. Surge load (microwave startup + fridge compressor) = 3000W.
Inverter Sizing:
Account for inverter efficiency (typically 90% or 0.90).
DC Current = AC Watts / (DC Voltage × Efficiency)
DC Current = 1500W / (12V × 0.90) = 138.8A continuous.
You need an inverter rated for at least 2000W continuous / 4000W surge to handle the 138A continuous draw without thermal shutdown. A Victron MultiPlus 12/3000/120 is the benchmark here, handling 3000W continuous and massive surge loads.
Charger Sizing & Charge Limits: Batteries have strict charge acceptance limits.
- Lead-Acid Limit: Max charge rate is 0.2C (20% of Ah). For a 400Ah bank, max charge is 80A.
- LiFePO4 Limit: Max charge rate is typically 0.5C to 1C. For a 400Ah bank, max charge is 200A to 400A.
Decision Path: Picking Your Battery Chemistry and BMS
Stop guessing and follow this decision tree to select the exact electrical charge reservoir for your build.
| If your constraint is... | Then choose this chemistry... | Required BMS / Monitoring |
|---|---|---|
| Budget under $400, weight doesn't matter, occasional weekend use | Flooded Lead-Acid (FLA) | Victron SmartShunt (for DoD tracking), no internal BMS. |
| Daily deep cycling, strict space/weight limits, solar off-grid | LiFePO4 (Lithium Iron Phosphate) | Internal BMS mandatory, plus a shunt for cell-level telemetry. |
| Extreme cold charging (below 0°C / 32°F) without heated enclosures | LiFePO4 with internal heating pads | BMS with low-temp charge cutoff and auto-heating triggers. |
For 90% of DIY off-grid, RV, and marine builds in 2026, the optimal pick is the SOK 12V 100Ah LiFePO4 battery (approx. $299). It features a robust internal BMS that handles low-temperature charge cutoffs, supports 1C discharge (100A continuous), and allows 4S4P configurations for massive 48V banks. Pair it with a Victron SmartShunt 500A/50mV to accurately track the Coulombs flowing in and out, ensuring you never violate your 80% DoD limit.
Understanding electrical charge is not just academic physics; it is the exact math that keeps your wires from melting, your BMS from tripping, and your lights on when the grid goes down. Calculate your Coulombs, respect the Peukert curve, and size your copper accordingly.
