 # How to understand discharge rate and lithium battery

## What Is C-rate?

The C-rate is a unit to declare a current value which is used for estimating and/or designating the expected effective time of battery under variable charge/discharge condition. The charge and discharge current of a battery is measured in C-rate. Most portable batteries are rated at 1C.

Observe how the charge and discharge rates are scaled and why it matters.

Charge and discharge rates of a battery are governed by C-rates. The capacity of a battery is commonly rated at 1C, meaning that a fully charged battery rated at 1Ah should provide 1A for one hour. The same battery discharging at 0.5C should provide 500mA for two hours, and at 2C it delivers 2A for 30 minutes. Losses at fast discharges reduce the discharge time and these losses also affect charge times.

A C-rate of 1C is also known as a one-hour discharge; 0.5C or C/2 is a two-hour discharge and 0.2C or C/5 is a 5-hour discharge. Some high-performance batteries can be charged and discharged above 1C with moderate stress. Table 1 illustrates the typical times at various C-rates. To calculate of load current value with charge/discharge rate, it can be obtained by;

∴ C-Rate (C) = Charge or Discharge Current (A) / Rated Capacity of Battery

Also, the expected available time of the battery on a given discharge capacity can be obtained by;

∴ Used hour of the battery = Discharge capacity (Ah) / Discharge current (A)

Discharge Capability of a high power Lithium cell.

[Example] In High Power products, rated capacity of the SLPB11043140H model is 4.8Ah. A Lithium-ion NMC cell.

1. What is 1C discharge current condition at this model?

∴ Charge (or discharge) Current (A) = Rated capacity of the battery * C-rate = 4.8 * 1(C) = 4.8 A

It’s means the battery is available for 1 hour by this current discharge condition.

2. The discharge current value under 20C discharge condition is 4.8(A)*20(C)=96A This battery reveals the excellent performance even if the battery discharges 20C discharge condition. The following is the available time of the battery when the capacity of a battery shows 4.15Ah

∴ Used hours (h) = Discharged capacity(Ah) / Applied current(A) = 4.15(Ah) / 96(A) ≒ 0.043hours ≒ 2.6 minutes with 96A

It means the battery can be used for 2.6minute (0.043h) with a load current of 96A ### Understanding Battery Capacity

The discharge rate provides you with the starting point for determining the capacity of a battery necessary to run various electrical devices. The product I x t is the charge Q, in coulombs, given off by the battery. Engineers typically prefer to use amp-hours to measure the discharge rate using time t in hours and current I in amps.

From this, you can understand battery capacity using values like watt-hours (Wh) which measure the battery’s capacity or discharge energy in terms of a watt, a unit of power. Engineers use the Ragone plot to evaluate the watt-hour capacity of batteries made of nickel and lithium. The Ragone plots show how to discharge power (in watts) falls off as discharge energy (Wh) increases. The plots show this inverse relationship between the two variables.

These plots let you use the battery chemistry to measure the power and discharge rate of different types of batteries including lithium-iron-phosphate (LFP), lithium-manganese oxide (LMO), and nickel manganese cobalt (NMC).

#### Battery Discharge Curve Equation

The battery discharge curve equation that underlies these plots let you determine the runtime of a battery by finding the inverse slope of the line. This works because units of watt-hour divided by watt give you hours of the runtime. Putting these concepts in equation form, you can write E = C x Vavg for energy E in watt-hours, capacity in amp-hours C, and Vavg average voltage of the discharge.

Watt-hours provide a convenient way to convert from discharge energy to other forms of energy because multiplying the watt-hours by 3600 to get watt-seconds gives you the energy in units of joules. Joules are frequently used in other areas of physics and chemistry such as thermal energy and heat for thermodynamics or the energy of light in laser physics.

A few other miscellaneous measurements are helpful alongside discharge rate. Engineers also measure the power capability in units of C, which is the amp-hour capacity divided by precisely one hour. You can also convert directly from watts to amps knowing that P = I x V for power P in watts, current I in amps, and voltage V in volts for a battery.

For example, a 4 V battery with a 2 amp-hour rating has a watt-hour capacity of 2 Wh. This measurement means you can draw the current at 2 amps for one hour or you can draw a current at a single amp for two hours. The relationship between current and time both depend on one another, as given by the amp-hour rating.

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