Ohmic resistance and polarization reduce battery energy efficiency by creating a voltage gap between the equilibrium open-circuit voltage and the measured terminal voltage. During charging, the tester must apply additional voltage to overcome the internal ohmic drop and electrochemical polarization. During discharge, those same effects consume part of the cell’s available voltage, reducing delivered energy and causing the cell to reach its voltage cutoff earlier.
Core takeaway: Ohmic resistance produces an immediate current-dependent voltage loss, while polarization represents slower electrochemical limitations such as charge-transfer and mass-transport resistance. Together, they increase charging energy, reduce discharge energy, and make round-trip energy efficiency lower than 100%.
How Battery Voltage Deviates from Equilibrium
Open-circuit voltage is the reference point
The equilibrium open-circuit voltage, (u_{OCV}), represents the cell’s thermodynamic voltage when no current flows and the cell has had sufficient time to approach equilibrium.
Once charging or discharging begins, the measured terminal voltage no longer equals (u_{OCV}). The difference reflects internal electrical and electrochemical losses.
Charging requires additional voltage
During charging, the applied terminal voltage can be represented conceptually as:
[ u_{ch} = u_{OCV} + u_R + u_P ]
Here, (u_R) is the ohmic voltage drop and (u_P) is the polarization voltage. The charger must supply both the energy associated with storing charge and the additional energy dissipated inside the cell.
At the energy level, this relationship is expressed as:
[ E_{O_ch} = E_{OCV} + E_{R_ch} + E_{P_ch} ]
Discharging delivers less than the equilibrium voltage
During discharge, the terminal voltage is lower than the equilibrium voltage:
[ u_{dch} = u_{OCV} - u_R - u_P ]
The cell therefore releases less usable electrical energy than its theoretical equilibrium behavior would suggest:
[ E_{O_dch} = E_{OCV} - E_{R_dch} - E_{P_dch} ]
The exact voltage losses vary with current, state of charge, depth of discharge, temperature, and cell condition.
How Ohmic Resistance Causes Energy Loss
The voltage drop appears immediately
Ohmic resistance produces an approximately instantaneous voltage change when current flows:
[ u_R = I R ]
The resistance includes electronic resistance, ionic resistance, current-collector resistance, contact resistance, and other resistive contributions within the cell and test path.
During discharge, the (IR) drop lowers the terminal voltage. During charge, the same effect raises the voltage that the charger must apply.
Dissipated power increases with current
The power converted primarily into heat by ohmic resistance is:
[ P_R = I^2R ]
This quadratic relationship is important in high-current testing. Doubling the current increases ohmic power loss by approximately four times if resistance remains constant.
As a result, high-rate operation can produce substantially lower discharge energy and higher charging losses even when the same amount of active material is involved.
Resistance can limit measured performance
In a discharge test, the voltage decline caused by (IR) brings the cell closer to its predefined cutoff voltage. At higher current, the cell may reach that cutoff sooner, reducing the measured capacity and output energy.
This reduction does not necessarily mean that the cell has lost an equivalent amount of active material. Some of the apparent capacity loss is caused by the voltage drop under load.
How Polarization Causes Energy Loss
Polarization is an electrochemical overvoltage
Polarization voltage is the deviation from equilibrium caused by electrochemical processes required to sustain current. It includes effects associated with activation, charge transfer, and concentration or mass transport.
Unlike a purely ohmic drop, polarization can develop over time and depend strongly on operating history.
Activation and charge-transfer limitations consume voltage
At the electrode interfaces, electrochemical reactions require a driving force beyond the equilibrium potential. This additional requirement appears as activation or charge-transfer polarization.
The result is a lower-than-equilibrium voltage during discharge and a higher-than-equilibrium voltage during charging.
Mass transport becomes important at high rates
At high current, reactants and ions may not be transported quickly enough to the reaction sites. Concentration gradients then develop, increasing polarization and causing the terminal voltage to fall more sharply during discharge.
In severe cases, reactant depletion near the electrode or the formation of compact discharged products can restrict ionic transfer. The cell reaches its cutoff voltage before its theoretical capacity has been fully accessed.
Polarization changes with depth of discharge
Polarization generally increases as discharge progresses. It may be modest at shallow depth of discharge, increase gradually through the middle range, and rise sharply near depletion.
This behavior explains why a cell can show a relatively stable voltage for much of a test and then experience a rapid voltage collapse near the end of discharge.
How These Losses Reduce Round-Trip Efficiency
Charging energy is increased
The charger supplies energy at the terminal voltage, which includes the equilibrium voltage plus ohmic and polarization terms. Therefore, part of the input energy is stored electrochemically, while another part is dissipated or consumed by internal electrochemical inefficiencies.
[ E_{O_ch} > E_{OCV} ]
Discharge energy is reduced
The load receives energy at a terminal voltage reduced by internal voltage losses:
[ E_{O_dch} < E_{OCV} ]
The energy available to the external circuit is consequently lower than the energy required to charge the cell.
Round-trip efficiency falls below unity
The electrical round-trip energy efficiency is:
[ \eta_E = \frac{E_{O_dch}}{E_{O_ch}} ]
Because charging requires additional energy and discharge returns less usable energy, practical round-trip efficiency is below 1.
The gap becomes larger with increased current, elevated polarization, increased internal resistance, and operating conditions that restrict ion transport.
What Battery Testing Systems Actually Measure
Terminal voltage captures the combined effect
A battery tester normally measures terminal voltage and current while controlling the applied charge or discharge profile. The measured voltage includes the equilibrium contribution, ohmic drop, and polarization effects.
Separating these components requires tests such as current pulses, rest periods, impedance measurements, or model-based analysis.
Cutoff voltage can create an apparent capacity loss
Under standard terminal-voltage control, an individual cell with high polarization may reach the charge or discharge cutoff before the underlying electrochemical state would otherwise require termination.
The test system or battery management unit then ends the cycle. This produces a lower measured capacity even when some chargeable or dischargeable material remains inaccessible under that operating condition.
Rest periods reveal relaxation behavior
Polarization can decay during rest as concentration gradients relax and the cell moves toward equilibrium. The terminal voltage may therefore recover after the current is removed.
Evaluating consistency only under active load can misclassify cells because it combines persistent resistance with temporary polarization and relaxation effects.
Resistance parameters change during operation
Ohmic resistance may remain relatively stable over much of a discharge and rise near complete depletion. Polarization resistance, by contrast, can increase progressively as charge-transfer and mass-transport conditions deteriorate.
Tracking both parameters helps distinguish an immediate resistive limitation from a slower electrochemical limitation.
Understanding the Trade-offs
Higher current improves test speed but increases losses
High-current tests expose rate capability and power limitations more quickly. However, they also increase (I R) loss, amplify polarization, and can reduce the capacity and energy measured before cutoff.
A high-rate result should therefore be interpreted as performance under that specific load, not as a direct measurement of the cell’s theoretical capacity.
A lower voltage does not always mean permanent degradation
A voltage drop during discharge may result from reversible polarization rather than permanent loss of active material. Recovery during rest can indicate that some of the observed deviation was associated with temporary concentration gradients or electrochemical relaxation.
Repeated behavior across controlled conditions is more informative than a single loaded-voltage measurement.
Internal resistance is not one fixed value
The effective resistance depends on current, state of charge, depth of discharge, temperature, frequency for impedance measurements, and the time scale of the test.
Treating all voltage deviation as a single constant resistance can hide the distinction between ohmic, charge-transfer, and mass-transport losses.
Test fixtures can add measurement error
Contacts, current collectors, wiring, and compression conditions can contribute to the measured voltage drop. Poor or inconsistent electrode assembly and contact compression can therefore appear as cell resistance or increased polarization.
The test setup must be controlled when comparing cells or evaluating design changes.
Making the Right Choice for Your Goal
The most useful test method depends on whether the goal is energy accounting, power evaluation, or diagnosis.
- If your primary focus is round-trip energy efficiency: Integrate measured voltage and current over both charge and discharge, then compare input and output energy while recording current, temperature, and operating limits.
- If your primary focus is high-rate power capability: Use multiple current levels and examine how (IR) drop, polarization, cutoff timing, and delivered energy change with load.
- If your primary focus is cell consistency: Include controlled rest periods and relaxation measurements so temporary polarization is not mistaken for permanent resistance variation.
- If your primary focus is electrode or assembly optimization: Track ohmic and polarization contributions separately, then use the results to improve material formulation, electrode design, contact quality, and compression control.
- If your primary focus is battery-management limits: Evaluate voltage behavior across depth of discharge and current range to establish operating boundaries that account for premature cutoff under load.
Understanding the separate contributions of ohmic resistance and polarization turns a simple voltage curve into a practical explanation of where battery energy is being lost and how testing can improve the design.
Summary Table:
| Loss Mechanism | Cause | Impact on Charging | Impact on Discharging | Energy Efficiency Loss |
|---|---|---|---|---|
| Ohmic Resistance | Electronic/ionic resistance, contact resistance | Extra voltage required, increases charging energy | Terminal voltage drops, reduces deliverable energy | Loss proportional to I²R; increases with current |
| Polarization | Activation (charge-transfer) and concentration (mass transport) overvoltage | Higher charging voltage needed; slower electrochemical kinetics | Lower discharge voltage; may cause premature cut-off | Loss increases with depth of discharge and high current |
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