Resistance of a cell

Capacity, nominal voltage and internal resistance are the basic parameters determining the performance of the lithium ion cell. The two parameters capacity,C and voltage,V define the energy (E=C x V) of the cell, while the power depends on the internal resistance of the cell. For a power cell the resistance has to be of the order of milli ohms or lesser. The resistance depends on various factors and it changes with SOC, temperature of operation, the applied current and the cell age. There are several ways to measure the resistance of a lithium-ion cell:  

1. AC Internal resistance measurement: This method is a standard way to measure resistance and it involves applying a small AC voltage (Vac) to the cell and measuring the resulting AC current (Iac). The internal resistance of the cell can then be calculated using Ohm's law (ACIR = Vac/Iac). This method is generally accurate but requires specialized equipment which can generate ac frequency signal of 1000Hz and 100 mA. The signal applied is instantaneous and it can be assumed that neither the SOC of the cell doesn't change nor the heating of cell occur in this process.
   
2. DC load test: In this method, a pulse signal or step change is required to observe change in voltage and current, before and after step. The cell's resistance can then be calculated using Ohm's law, if Vi and Ii is the initial current before step and after step it is Vf and If, then DCIR = (Vi – Vf ) / (Ii – If). The applied step change in current can be a step up in current, which is a charge pulse, or it can be a step down in current, which is a discharge pulse. This method is relatively simple and can be done with a cycler, but the results may not be as accurate as the SOC or state of the cell changes when current is applied.
   
3. Electrochemical impedance spectroscopy (EIS): This method involves applying a small AC voltage with a large frequency spectrum (typically 1 mHz to 100 kHz) to the cell and measuring the resulting AC current. The cell's impedance (which is related to resistance) can be calculated from the measurements. EIS can provide detailed information about the cell's electrochemical processes and is often used in research and development. However, it requires specialized equipment and can be time-consuming.