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An empirical formula that describes how the available capacity of a battery decreases as the rate of discharge increases. The law is stated as [latex]C_p = I^k t[/latex], where [latex]C_p[/latex] is the capacity at a one-ampere discharge rate, [latex]I[/latex] is the discharge current, [latex]t[/latex] is the discharge time, and [latex]k[/latex] is the Peukert constant, specific to the battery type. It quantifies the inefficiency at high loads.
Peukert’s law provides a more accurate picture of battery capacity than the simple amp-hour rating, which is typically specified at a low, constant discharge rate. The law accounts for the fact that at high discharge rates, the battery becomes less efficient. This inefficiency stems from several factors. Firstly, the internal resistance of the battery causes energy to be lost as heat, a loss that increases with the square of the current ([latex]P_{loss} = I^2R[/latex]). This wasted energy is unavailable to the load.
Secondly, the electrochemical processes within the battery have finite speeds. At high discharge rates, the chemical reactions cannot keep pace, and the diffusion of ions within the electrolyte becomes a bottleneck. This leads to a depletion of reactants near the electrodes’ surfaces, causing the voltage to drop prematurely and cutting off the discharge before all the active material has been utilized. The unused material means the effective capacity delivered is lower.
The Peukert constant, [latex]k[/latex], is determined empirically and reflects how much a battery is affected by high discharge rates. A value of [latex]k[/latex] close to 1 indicates an ideal battery that is not significantly affected by the discharge rate. Lead-acid batteries have a relatively high [latex]k[/latex] (typically 1.1 to 1.3), while modern 锂离子电池 have a [latex]k[/latex] much closer to 1 (e.g., 1.05), indicating their superior performance under heavy loads.
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