Consider a 4680 Lithium ion battery. When the electrode sheet is unrolled, the footprint area is 8 cm x 6.25 m for a single electrode. Based on these values, you will understand what contribute most to the internal resistance of a battery, and why tab-less design is important. Assume that the transport distance is 50 um, the porosity is 30%, the turtuosity is 4.5, and the ionic conductivity of the electrolyte at 25 degrees C is 5 mS/cm.

1) Calculate the electrolyte resistance 2) Calculate the electronic resistance of the current collector under conditions (a) and (b). Take the current collector of the negative electrode as an example. It is Cu with a thickness of 6 um. Cu has an electronic conductivity of 6 x 10⁵ S/cm. (a) Calculate the electronic resistance of the current collector where all electronic currents accumulate to one end of the current collector. This means that there is only one tab at the short side of the sheet, and current flow in parallel to the long side. Account for the location-dependent current.

(b) Calculate the electronic resistance of the current collector in a tab-less design, which is used in Tesla 4680 cell, where current flows along the short side of the electrode sheet. Account for the location-dependent current.

3) Calculate the charge transfer resistance at a current of 15 A under the following conditions/assumptions: Let us just take a look at the negative electrode with a specific capacity of 360 mAh/g. Assume all electrode particles have a surface area of 0.1 m²/g, a cell capacity of 27 Ah, an exchange current density of 0.1 mA/cm2, a transfer coefficient of 0.5, and temperature at 300 K.