Within battery design there are a number of electrical formulas that we should know. Hence a page collecting them together.
Ohm’s Law
Defines the relationship between voltage, V (volts), current, I (amps), and resistance, R (Ohms) in an electrical circuit. This states that current is directly proportional to voltage and inversely proportional to resistance:
Power Law
The electrical power law states that power, P (watts) equals voltage, V (volts) multiplied by current, I (amperes). It defines the rate at which electrical energy is transferred or consumed.
It is useful to express the power in terms of current and resistance, R (Ohms).
Electrical Energy
Electrical energy, E (Joules) is the capacity to do work through the movement of charges, calculated as power multiplied by time, t (seconds):
Again, it is useful to express the energy in terms of current, resistance and time.
Using these equations we can make estimates of the electrical performance of a cell and battery pack.
Calculated Peak Power
For most simple peak power calculations we will be interested in the Direct Current Internal Resistance (DCIR) value for a new cell at 50% SOC (25°C, 10s), Open Circuit Voltage (OCV) and minimum voltage. Note: this is just an estimation and this needs to be compared to the manufacturers specifications and tested values.
However, as an estimate it is a good starting point.
We can also use this to estimate the current demand from a pack from the power versus time profile given the cell resistance and open circuit voltage.
We are often given a power demand for a battery cell or pack.
However, what is the current that flows for that given power requirement? We can solve this if we know the open circuit voltage and the internal resistance of the pack.