Battery Discharge Curves: How C-Rate Affects Capacity

simulator intermediate ~10 min
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~185 Wh delivered from 50Ah Li-ion at 1C

A 50Ah lithium-ion battery discharged at 1C (50A) delivers approximately 185 Wh over about 55 minutes. Voltage starts at ~4.2V and drops to the 3.0V cutoff, with a plateau around 3.7V.

Formula

Peukert's law: C = I^k × t (k = Peukert exponent)
C-rate: I = C_rate × Capacity_Ah
Energy delivered: E = ∫V(t)·I dt (area under V-t curve × current)

Voltage Under Load

A battery's voltage is not constant — it drops as the battery discharges, following a characteristic curve that depends on chemistry, load current, and temperature. Lithium-ion cells start at ~4.2V and drop to a 3.0V cutoff. Lead-acid starts at ~12.7V (6 cells) and drops to ~10.5V. Understanding these curves is essential for designing battery-powered systems that perform reliably across the full charge range.

The C-Rate Trade-Off

Discharging a battery faster (higher C-rate) means less of its nominal capacity is actually usable. A battery rated at 50Ah at the 20-hour rate (2.5A) might deliver only 40Ah at the 1-hour rate (50A). Internal resistance causes voltage to sag under load, reaching the cutoff voltage sooner. This effect is captured by Peukert's law, first described in 1897 for lead-acid batteries.

Chemistry Matters

Different battery chemistries produce dramatically different discharge curves. Lithium-ion (NMC) has a sloping curve that makes voltage a useful state-of-charge indicator. LiFePO4 is extremely flat — great for stable output but challenging for charge estimation. Lead-acid has a gradual slope with a steep drop-off near depletion. Each chemistry trades off energy density, cycle life, safety, and cost.

Temperature and Real-World Performance

Battery performance in the real world often disappoints compared to datasheet specifications measured at 25°C. At -10°C, a lithium-ion battery may lose 30% of its capacity. At 45°C, degradation accelerates. This simulation lets you explore how C-rate, chemistry, and temperature interact to determine actual delivered energy — the number that matters for system design.

FAQ

What is a C-rate?

C-rate describes the discharge (or charge) speed relative to battery capacity. 1C means the entire capacity is discharged in 1 hour (50A from a 50Ah battery). 0.5C takes 2 hours, 2C takes 30 minutes. Higher C-rates reduce usable capacity due to internal resistance losses.

What is Peukert's law?

Peukert's law states that battery capacity decreases with increasing discharge rate: C = I^k × t, where k is the Peukert exponent (1.0 for ideal, ~1.1-1.3 for lead-acid, ~1.02-1.05 for lithium). Higher k means more capacity loss at high currents.

Why do batteries lose capacity in cold weather?

Cold temperatures slow the chemical reactions inside batteries and increase internal resistance. Lithium-ion batteries can lose 20-40% capacity at -10°C compared to 25°C. Electrolyte viscosity increases, ion mobility decreases, and charge transfer resistance rises.

What makes LiFePO4 discharge curves different?

LiFePO4 (lithium iron phosphate) has an exceptionally flat discharge curve — voltage stays near 3.2V for 80%+ of the discharge. This makes it easier to estimate remaining capacity but harder to use voltage as a state-of-charge indicator.

Sources

Embed

<iframe src="https://homo-deus.com/lab/energy-systems/battery-discharge/embed" width="100%" height="400" frameborder="0"></iframe>
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