Understanding C-rate

Let’s get the basics right for C rate.

If someone says to you that they are supplying a 100Ah battery, then it has no meaning. It is incomplete information. It is like a shopkeeper saying to you, “I will give you 2 Oil”. Whether it is 2 liters of Oil or 2 bottles of Oil has not been specified. Similarly, the capacity of a battery (Ah) should always be specified along with its C rate. So, for example, the correct way of specifying battery capacity would be 100Ah @ C20.

C-rate is basically the charging rate or discharging rate of batteries. In other words, C-rate is used to scale the charge and discharge current of a battery. For a given capacity, C-rate is a measure that indicates at what current a battery is charged and discharged to reach its defined capacity.

A 1C rate (or C/1) means that the discharge current will discharge the entire battery in 1 hour. For a battery with a capacity of 100Ah, this equates to a discharge current of 100A.

Similarly, a 1C (or C/1) charge loads a 100Ah battery at 100A in 1 hour, so at the end of the hour the battery reaches a capacity of 100Ah; a 1C (or C/1) discharge drains the battery at that same rate.

A 0.5C or (C/2) charge loads a 100Ah battery at 50A so it takes 2 hours to charge the battery at the rating capacity of 100Ah;

A 2C charge loads a 100Ah battery at 200A, so it takes theoretically 30 minutes to charge the battery at the rating capacity of 100Ah;

Last example: A lead acid battery with a C10 (or C/10) rated capacity of 300Ah should be charged or discharged in 10 hours with a current charge or discharge of 30A.

Note that though a battery is rated as 300Ah @ C10, it does not mean that you cannot draw more than 30A. You can still draw more current like 60A but remember that the battery capacity will reduce if you keep on doing this due to Peukert’s law.

To understand this, let’s look at the datasheet of a Sealed lead-acid battery advertised as a 100Ah @ C20. This is the US AGM 31 by US battery.

If you observe the above table, you can notice that this 100Ah battery is also a 92Ah battery @ C10 (or 10-hour rate) and 105Ah battery @ C48 (or 48-hr rate). Thus specifying just the Ah capacity is only half the story. You need to specify both the Ah and C-rate of the battery.

Why is it important to know the C-rate or C-rating of a battery?

C-rate is an important data for a battery because for most of batteries the energy stored or available depends on the speed of the charge or discharge current. Generally, for a given capacity, you will have less energy if you discharge in 1 hour than if you discharge in 20 hours, reversely you will store less energy in a battery with a current charge of 100 A during 1 h than with a current charge of 10 A during 10 h.

In the above US AGM 31, the 100Ah battery @ C20 will have less energy (only 66Ah) if you discharge in 1 hr (or C/1 rate) and store less energy (only 92Ah) with a current charge of 10A during 10h (or C10 rate).

C-rate notations

You would have noticed till now that the numbers are placed either to the left or right of C. In addition, C10 batteries are also represented as C/10. So what is the correct way of representing the C rate? To understand this, please refer to the below video:

Basically, C10 and C/10 are the same. In India, we normally use C10 without the “/” when the number is placed to the right of C.

So now you can see as the C-rating increases (on the right of C), the ampere limit decreases but the number of hours increases. C20 battery is a medium discharge battery, it is recommended for household on mains inverter because the power outage is usually long. C10 is fast discharge battery will not withstand a long power outage and we do not need high (15A) and the inverter connected appliances are usually light, electronics, fan etc they do not need high current.

A C10 should not be discharged in less than 10 hours, C20 should not be discharged in less than 20 hours. So C20 gives us more time before it can be fully discharged. C10 is recommended for solar but it will not last long as C20. C10 should not be discharged within 10 hours and C20 should not be discharged in less than 20 hours

Similarly, C20 should not be fully charged from empty less than 20 hours, C10 should not be charged in less than 10 hours from empty. This allows C10 to quickly charge when sun is available. In certain applications even C5 batteries are used it is a rapid discharge battery but charges even rapidly.

So why does the capacity decrease at higher C rate?

Battery voltage includes mainly 3 contributions: difference between chemical potentials of the electrodes (well-known equation ΔG=-zFE) and two electrical potentials of the double layers at the surface of each electrode. The potential of the double layer includes the equilibrium part and the part caused by the finite rate of transfer of ions between the electrodes and electrolyte (so-called overpotential). Battery capacity is the amount of transferred ions, so it is directly related to the chemical composition of the electrodes and their chemical potentials.

If we charge the battery to the same voltage at two different rates, the overpotential will be higher for the battery charged at the higher rate. Correspondingly, the difference between the chemical potentials will be lower (we fix only the sum of all contributions to voltage!) and amount of the transferred ions will be lower, meaning that the capacity will be lower.