Internal AC resistance is usually stable through the first half of discharge, then rises as the battery approaches depletion. In tubular-plate lead-acid and pocket-plate nickel-cadmium batteries, resistance remains relatively constant until approximately 50% depth of discharge (DOD). Beyond that point it increases, with Ni/Cd showing a much sharper rise near end of discharge and lead-acid exhibiting a more gradual increase.
Battery sizing cannot rely on a single nominal resistance value. The resistance profile across state of charge determines voltage drop, heat generation, available fault current, fuse behavior, pulse power, and the point at which a battery can no longer support the system load.
Why Internal Resistance Changes During Discharge
The early discharge region is relatively predictable
At low to moderate DOD, both tubular-plate lead-acid and pocket-plate Ni/Cd batteries generally maintain a nearly stable internal AC resistance. This produces comparatively consistent voltage response under a given load.
This stable region is useful for normal operating estimates, but it should not be mistaken for the behavior of the entire discharge cycle.
Deep discharge increases resistance
After roughly 50% of capacity has been drawn, internal resistance begins to rise. The increase reflects changes in the electrode active materials and electrolyte conditions as the cell approaches its discharged state.
Because the resistance is higher, the same load current produces a larger voltage deviation:
[ \Delta V = I \times R ]
The battery may therefore reach the system's low-voltage cutoff before its theoretical electrochemical capacity has been fully extracted.
Ni/Cd and lead-acid batteries do not change in the same way
Near the end of discharge, Ni/Cd resistance can increase suddenly and sharply. Lead-acid resistance generally rises more progressively, giving a less abrupt transition into poor load performance.
This distinction matters when a system has little voltage margin. A Ni/Cd battery may support its load adequately and then experience a rapid loss of voltage capability, while a lead-acid battery may show a more gradual deterioration.
How Resistance Affects Battery System Sizing
Voltage drop must be calculated at the relevant DOD
A sizing calculation based only on fresh, fully charged, or mid-discharge resistance can understate the voltage drop at the end of the required backup period. The design should use the resistance corresponding to the battery's expected state of charge, temperature, discharge rate, and measurement conditions.
For high-current loads, even a modest resistance increase can create a substantial additional voltage drop.
Protective fuse sizing depends on available current
Internal resistance limits the current that a battery can deliver during a fault. As resistance rises during discharge, the prospective DC short-circuit current falls.
This affects the selection and coordination of:
- DC fuse interrupting ratings
- Fuse time-current behavior
- Circuit-breaker operation
- Cable fault withstand requirements
- Protection discrimination
Protection must account for both conditions: the high fault current available from a charged, low-resistance battery and the lower current available after significant discharge. A fuse that is appropriate for normal operating current may not provide the intended protection across the full resistance range.
Backup duration is limited by load voltage, not capacity alone
A battery can contain remaining chemical capacity while being unable to maintain the minimum voltage required by the connected equipment. Rising resistance causes the loaded voltage to fall further below open-circuit voltage.
Consequently, usable capacity depends on the system cutoff voltage and load current. The rated ampere-hour value by itself is insufficient for sizing a battery system.
Thermal effects become more important at high current
Internal power dissipation is approximately:
[ P_{\text{loss}} = I^2R ]
As resistance rises, the battery converts more input energy into heat during discharge. This reduces efficiency and can intensify thermal stress, particularly in high-current or repeated-pulse applications.
Temperature also influences resistance. Lower ambient temperature generally increases resistance because electrolyte ionic conductivity decreases, so cold-condition sizing may be more restrictive than room-temperature sizing.
How Resistance Affects Dynamic Power Delivery
High resistance reduces terminal voltage
The terminal voltage under load is lower than the open-circuit voltage because of ohmic resistance and electrochemical polarization. At normal operating currents, the ohmic component can be a primary contributor to this difference.
At very high discharge rates, concentration and mass-transport limitations can become dominant. A complete performance model therefore needs to distinguish resistance-related voltage drop from other polarization losses.
Pulse performance changes with state of discharge
During a short pulse, the battery must provide current without allowing its terminal voltage to fall below the equipment limit. As DOD increases and internal resistance rises, the available pulse power decreases.
Longer pulses usually produce greater voltage loss because electrochemical and transport limitations have more time to develop. A battery that passes a short pulse test may still fail a longer-duration load requirement.
Operating voltage limits can shorten practical battery life
Equipment with a narrow acceptable voltage range is especially sensitive to resistance growth. The system may shut down while significant nominal capacity remains, particularly during deep discharge or high-current operation.
Voltage regulation, a larger battery configuration, lower-current architecture, or a chemistry with a flatter discharge response may be required when the load cannot tolerate this behavior.
How to Characterize the Resistance Profile
Test across the complete discharge range
Resistance should be measured at multiple DOD points rather than reported as a single nominal value. At minimum, testing should cover:
- Fully charged condition
- The relatively flat early-to-mid discharge region
- The transition near approximately 50% DOD
- Deep discharge
- The end-of-discharge region
For Ni/Cd batteries, finer sampling near end of discharge is particularly important because the resistance increase can be abrupt.
Control the test conditions
Resistance measurements are meaningful only when their conditions are recorded. Characterization should specify:
- Battery temperature
- Rest time before measurement
- Charge and discharge history
- Test current or signal amplitude
- AC signal frequency
- Measurement duration
- Battery age and condition
- Number of cells and connection configuration
AC resistance is frequency-dependent and does not necessarily equal the effective resistance observed during a long DC discharge. The measurement method must therefore match the engineering question.
Separate AC resistance from dynamic resistance
A small-signal AC measurement describes impedance behavior around a particular operating point and frequency. A dynamic resistance measurement, often represented as:
[ R_{\text{dynamic}} = \frac{\Delta V}{\Delta I} ]
describes the voltage response to a current change and can include ohmic, polarization, and time-dependent effects.
Neither measurement should automatically be substituted for the other in a sizing calculation. AC resistance is useful for repeatable state-of-health and state-of-charge comparisons, while dynamic load testing is more representative of protection and power-delivery behavior.
Measure loaded voltage and temperature as well
Resistance data is most useful when paired with terminal voltage, current, DOD, and temperature. This allows engineers to determine whether a voltage decline is primarily caused by resistance growth, polarization, thermal effects, or mass-transport limitations.
The result should be a performance map, not just a resistance number.
Understanding the Trade-offs
A single resistance value is convenient but incomplete
Using one nominal resistance simplifies calculations, but it can conceal the sharp rise that occurs during deep discharge. This is especially risky for high-current loads, narrow voltage windows, and systems requiring full rated backup duration.
A resistance curve adds testing effort but provides a more defensible basis for system design.
AC measurements are repeatable but application-dependent
AC resistance is valuable for battery comparison and condition monitoring, yet its result depends on signal frequency, amplitude, temperature, and instrumentation. It may not reproduce the voltage response during a seconds-long pulse or a sustained DC load.
The correct measurement is the one that represents the system event being analyzed.
More capacity does not always solve a voltage problem
Adding parallel capacity reduces the current demanded from each cell and can reduce system-level voltage drop. However, it does not eliminate the underlying resistance increase of a deeply discharged cell, and it may introduce current-sharing, protection, and balancing considerations.
The battery configuration must be evaluated together with the load profile and cutoff requirements.
Chemistry-specific behavior must remain visible
Applying a generic end-of-discharge resistance curve to every battery type can produce incorrect conclusions. The gradual lead-acid rise and the sharper Ni/Cd rise require different sampling density, voltage-margin assumptions, and end-of-discharge models.
Making the Right Choice for Your Goal
Select the resistance data and test method according to the failure mode the system must avoid.
- If your primary focus is backup-duration sizing: Use loaded voltage and resistance data across the complete DOD range, including the deep-discharge region and the required temperature range.
- If your primary focus is fuse and protection coordination: Evaluate the lowest-resistance, fully charged condition for maximum fault current and the higher-resistance discharged condition for minimum prospective current.
- If your primary focus is pulse-power capability: Perform dynamic current-step or pulse testing at several DOD and temperature points rather than relying only on small-signal AC resistance.
- If your primary focus is battery characterization or health monitoring: Track AC resistance under controlled frequency, temperature, rest-time, and state-of-charge conditions, and interpret trends using chemistry-specific profiles.
- If your primary focus is high-current efficiency and thermal design: Include the (I^2R) loss associated with resistance growth and verify that cell temperature remains within the permitted operating range.
Accurate battery-system design requires a resistance-versus-discharge profile that reflects the chemistry, operating conditions, and actual electrical demands of the application.
Summary Table:
| DOD Range | Resistance Behavior | Key Implication |
|---|---|---|
| 0-50% | Stable, nearly constant | Predictable voltage drop for normal loads |
| 50-80% | Gradual increase (lead-acid) or sharp increase (Ni/Cd) | Voltage margin shrinks, capacity may be limited |
| 80-100% | Significant rise | End-of-discharge voltage collapse risk, protection coordination affected |
At KINTEK, we provide advanced battery testing and characterization equipment to accurately measure resistance profiles across DOD, ensuring your systems are optimally sized and protected. From our cutting-edge impedance analyzers to comprehensive battery cyclers, we support your R&D in lead-acid, Ni/Cd, and other chemistries. Contact us today to enhance your battery reliability and performance — get in touch!