Battery Discharge Simulator: Voltage, Capacity, and Runtime

simulator intermediate ~10 min
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Runtime ≈ 3.0 h — at 3.65 V terminal voltage

A 3.0 Ah lithium-ion cell discharged at 1 A runs for approximately 3 hours. The voltage starts at 3.65 V (after IR drop) and follows a characteristic plateau before dropping steeply near end of discharge.

Formula

V_terminal = V_ocv(SOC) − I × R_internal
Runtime = Capacity / I (ideal, in hours)
Energy = ∫ V(t) × I dt (watt-hours)

The Shape of Stored Energy

A battery's discharge curve is its fingerprint. It reveals how voltage declines as charge is extracted, and its shape depends on the underlying electrochemistry. Lithium cobalt oxide cells (in phones) show a smooth downward slope, while lithium iron phosphate cells (in EVs) maintain a flat plateau until suddenly dropping. Understanding these curves is essential for predicting runtime, designing battery management systems, and comparing cell chemistries.

Internal Resistance and IR Drop

The moment current flows, the terminal voltage drops below the open-circuit voltage by I × Rᵢ. This IR drop is instantaneous and proportional to current. In high-power applications like power tools or electric vehicles, minimizing internal resistance is critical. Cell aging, low temperature, and manufacturing defects all increase Rᵢ, degrading performance.

State of Charge and Voltage

As the battery discharges, the active materials at both electrodes change composition. This shifts the thermodynamic equilibrium voltage. In the middle of discharge, voltage changes gradually (the plateau region), but near the endpoints — fully charged and fully depleted — voltage changes rapidly. Battery management systems use this voltage-SOC relationship to estimate remaining charge.

Energy vs. Power

A battery optimized for energy (high capacity, thin electrodes) differs fundamentally from one optimized for power (low resistance, thick current collectors). This simulation shows the tradeoff: increasing load current increases instantaneous power but reduces total delivered energy through greater resistive losses and the Peukert effect.

FAQ

What is a battery discharge curve?

A discharge curve plots terminal voltage against time (or state of charge) as a battery delivers current. Different chemistries have characteristic shapes: lithium-ion shows a gradual slope, while lithium iron phosphate has a flat plateau. The curve reveals usable capacity, cutoff voltage, and energy delivery.

What is C-rate?

C-rate expresses current relative to capacity. 1C means the current that would fully discharge the battery in one hour (e.g., 3 A for a 3 Ah cell). 2C doubles that rate (6 A), and C/2 halves it (1.5 A). Higher C-rates increase internal losses.

Why does voltage drop during discharge?

Voltage drops for two reasons: IR drop (V = IR across internal resistance, instantaneous) and electrochemical depletion (as active material is consumed, the open-circuit voltage decreases). Both effects accelerate near end of discharge.

What is Peukert's effect?

Peukert's effect describes how higher discharge currents reduce the effective capacity of a battery. A cell rated at 3 Ah at low current may deliver only 2.5 Ah at high current because faster discharge causes concentration gradients and increased losses inside the cell.

Sources

Embed

<iframe src="https://homo-deus.com/lab/electrochemistry/battery-discharge/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub