The Core Physics: Relation Between Current and Charge in Battery Systems
The fundamental relation between current and charge is defined by the equation Q = I × t. In practical electrical terms, current (measured in Amps, or I) is the instantaneous rate of electron flow, while charge (measured in Amp-hours, or Q) is the total volume of electrons delivered over a specific time (t). If you draw 10 Amps of current from a battery for 5 hours, you have consumed 50 Amp-hours (Ah) of charge.
Think of it like a municipal water system: current is the flow rate through the pipe (gallons per minute), and charge is the total capacity of the water tower (gallons). You cannot size a battery bank or select wire gauges without understanding how your load's current draw depletes the battery's total charge capacity over time.
To apply this to a real power system, we must trace the energy from source to load. A standard off-grid or backup system block follows this exact path:
- Source: Battery Bank (stores chemical charge, outputs DC current).
- Protection: Class T Fuse or DC Breaker (interrupts fault current; sized 1.25× max continuous current).
- Distribution: Copper Busbars and 2/0 AWG or 4/0 AWG welding cable (carries current with minimal voltage drop).
- Conversion: Inverter/Charger (converts DC current to AC current; manages AC-to-DC charging).
- Load: AC Subpanel and appliances (consumes AC power).
Series vs. Parallel: Consequences for Voltage and Amp-Hours
When building a battery bank to hold a specific charge, you must wire cells in series, parallel, or a combination. The relation between current and charge shifts dramatically depending on your topology.
| Configuration | Voltage Consequence | Amp-Hour (Charge) Consequence | Max Current Output |
|---|---|---|---|
| Series | Voltages add (e.g., 4× 12V = 48V) | Ah remains identical to a single cell | Same as single cell |
| Parallel | Voltage remains identical to a single cell | Ah adds (e.g., 4× 100Ah = 400Ah) | Current capacity multiplies |
| Series-Parallel | Series string voltages add | Parallel string Ah capacities add | Multiplied by parallel strings |
Sizing Math: Peukert’s Law, Efficiency, and C-Rate Limits
Theoretical charge (Q = I × t) assumes 100% efficiency and linear chemistry. Real-world batteries suffer from conversion losses and chemical limitations. Let's size a system for a 1,500W continuous space heater running for 3 hours on a 12V nominal system.
1. Calculate True DC Current Draw
Inverters are not perfectly efficient. Assuming a 90% inverter efficiency at this load, the DC current drawn from the battery is:
I = P / (V × Efficiency)
I = 1500W / (12V × 0.90) = 138.8 Amps
2. Calculate Required Charge (Amp-Hours)
For 3 hours of runtime, the theoretical charge required is:
Q = 138.8A × 3h = 416.4 Ah
3. Apply Peukert’s Law (Lead-Acid/AGM)
If you use AGM lead-acid batteries, Peukert's Law dictates that as current draw increases, the usable charge capacity drops non-linearly. A 400Ah AGM bank rated at the 20-hour rate (a 20A draw) will only deliver roughly 220Ah of usable charge when hit with a 138A continuous draw. To get 416Ah of real-world capacity at this high current, you would need to parallel nearly 800Ah of rated AGM batteries, and you still haven't accounted for Depth of Discharge (DoD). Lead-acid should not be discharged past 50% DoD without severe cycle-life degradation, meaning you'd need a 1,600Ah AGM bank.
4. Apply C-Rate and DoD Limits (Lithium LiFePO4)
Lithium Iron Phosphate (LiFePO4) batteries do not suffer from Peukert's effect; a 400Ah LiFePO4 bank will deliver very close to 400Ah regardless of the draw. However, you must respect the C-rate (charge/discharge rate limit) and DoD.
- Discharge C-Rate: Most LiFePO4 cells are rated for 1C continuous discharge. A 100Ah battery can safely output 100A. To sustain our 138.8A draw, we need a minimum of two 100Ah batteries in parallel (yielding 200A max capacity).
- Charge C-Rate: Typically limited to 0.5C. A 200Ah bank can only accept 100A of charging current from your solar controller or generator.
- DoD: LiFePO4 can safely be discharged to 80-90% DoD. A 400Ah LiFePO4 bank gives you ~360Ah of usable charge, easily covering our 416Ah requirement if we bump to a 48V architecture.
Inverter and Charger Sizing for Your Target Load
Once you understand the relation between current and charge for your load, you must size the conversion equipment to handle the peak current without tripping internal breakers or bottlenecking the recharge cycle.
Inverter Sizing:
Your continuous load is 1,500W. While a 2,000W inverter technically covers this, inverters operate at peak efficiency (typically 93-95%) when loaded between 30% and 70% of their rated capacity. Furthermore, if you ever add an inductive load (like a well pump or refrigerator compressor), you need surge headroom. Rule of thumb: Size the inverter at 2× your maximum continuous resistive load. For a 1,500W heater, select a 3,000W to 4,000W pure sine wave inverter.
Charger Sizing:
To recharge a depleted battery bank in a reasonable timeframe without violating the charge C-rate, size your AC-to-DC battery charger at 10% to 20% of the battery bank's total Ah capacity. If you build a 200Ah LiFePO4 bank (max 0.5C charge limit = 100A), your charger should output between 40A and 80A. An 80A charger will replenish a fully depleted 200Ah bank in roughly 2.5 hours (accounting for the constant-voltage absorption taper at the top of the charge cycle).
Decision Tree: Selecting Your Battery Chemistry and Configuration
Use this decision matrix to terminate your design phase and select the exact hardware for your system. This path assumes a daily-cycled off-grid or backup scenario with loads exceeding 1,500W.
| System Constraint | If True... | If False... |
|---|---|---|
| Is the continuous load > 1,200W? | Proceed to 48V architecture evaluation. | 12V architecture is acceptable; use 12V LiFePO4. |
| Will the system cycle daily (>300 cycles/year)? | LiFePO4 is mandatory for ROI and DoD. | AGM/Gel is acceptable for standby/emergency use. |
| Is the installation indoors or in a living space? | Must comply with NFPA 855 spacing and BMS requirements. | Outdoor/shed installs have more flexible spacing. |
| Do you need to parallel more than 4 batteries? | Switch to high-capacity server-rack batteries. | Standard 12V drop-in Group 24/31 cases are fine. |
The Concrete Pick: 48V Server Rack Architecture
For a robust, daily-cycled system handling 1,500W+ loads, 12V is mathematically inefficient and AGM is economically unviable due to Peukert losses and 50% DoD limits. The definitive, decision-forward choice is a 48V LiFePO4 Server Rack Battery.
Recommended Hardware Configuration:
- Battery: EG4 48V 100Ah Server Rack LiFePO4 (Part# EG4-48V-100AH). This single module provides 5.12kWh of charge. It features a 100A BMS (0.2C to 1C discharge), built-in low-temp cutoff, and RS485/CAN communication to talk directly to the inverter.
- Scaling: Wire two of these in parallel for a 48V 200Ah bank (10.24kWh total charge, 200A max continuous discharge). This easily covers our 34.7A continuous draw with massive headroom for surges.
- Inverter/Charger: Growatt 5000W 48V All-in-One (or equivalent Victron MultiPlus-II 48/5000). The 5000W rating keeps your 1500W load right in the 30% efficiency sweet spot, and the integrated 80A AC charger perfectly matches the 0.4C charge rate for a 200Ah bank.
- Protection: 150A Class T fuse on the positive battery lead, sized to protect the 2 AWG battery cables and the BMS.
By respecting the physical relation between current and charge, accounting for inverter efficiency, and moving to a higher voltage to suppress current, you eliminate cable heating, bypass Peukert penalties, and build a system that will reliably deliver power for over 4,000 cycles. For deeper wiring schematics and busbar sizing, consult the Victron Energy Wiring Unlimited handbook, which remains the industry benchmark for DC system architecture.
