What is the power output of a 1.5 v ideal battery which is delivering a current of 0.2 a

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 typical times at various C-rates.

C-rate	Time
5C	12 min
2C	30 min
1C	1h
0.5C or C/2	2h
0.2C or C/5	5h
0.1C or C/10	10h
0.05C or C/20	20h

Table 1: C-rate and service times when charging and discharging batteries of 1Ah (1,000mAh)

The battery capacity, or the amount of energy a battery can hold, can be measured with a battery analyzer. (See BU-909: Battery Test Equipment) The analyzer discharges the battery at a calibrated current while measuring the time until the end-of-discharge voltage is reached. For lead acid, the end-of-discharge is typically 1.75V/cell, for NiCd/NiMH 1.0V/cell and for Li-ion 3.0V/cell. If a 1Ah battery provides 1A for one hour, an analyzer displaying the results in percentage of the nominal rating will show 100 percent. If the discharge lasts 30 minutes before reaching the end-of-discharge cut-off voltage, then the battery has a capacity of 50 percent. A new battery is sometimes overrated and can produce more than 100 percent capacity; others are underrated and never reach 100 percent, even after priming.

When discharging a battery with a battery analyzer capable of applying different C rates, a higher C rate will produce a lower capacity reading and vice versa. By discharging the 1Ah battery at the faster 2C-rate, or 2A, the battery should ideally deliver the full capacity in 30 minutes. The sum should be the same since the identical amount of energy is dispensed over a shorter time. In reality, internal losses turn some of the energy into heat and lower the resulting capacity to about 95 percent or less. Discharging the same battery at 0.5C, or 500mA over 2 hours, will likely increase the capacity to above 100 percent.

To obtain a reasonably good capacity reading, manufacturers commonly rate alkaline and lead acid batteries at a very low 0.05C, or a 20-hour discharge. Even at this slow discharge rate, lead acid seldom attains a 100 percent capacity as the batteries are overrated. Manufacturers provide capacity offsets to adjust for the discrepancies if discharged at a higher C rate than specified. (See also BU-503: How to Calculate Battery Runtime) Figure 2 illustrates the discharge times of a lead acid battery at various loads expressed in C-rate.

Figure 2: Typical discharge curves of lead acid as a function of C-rate

Smaller batteries are rated at a 1C discharge rate. Due to sluggish behavior, lead acid is rated at 0.2C (5h) and 0.05C (20h).

While lead- and nickel-based batteries can be discharged at a high rate, the protection circuit prevents the Li-ion Energy Cell from discharging above 1C. The Power Cell with nickel, manganese and/or phosphate active material can tolerate discharge rates of up to 10C and the current threshold is set higher accordingly.

Last Updated: 25-Oct-2021

Batteries In A Portable World

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A battery’s charge and discharge rates are controlled by battery C Rates. The battery C Rating is the measurement of current in which a battery is charged and discharged at. The capacity of a battery is generally rated and labelled at the 1C Rate (1C current), this means a fully charged battery with a capacity of 10Ah should be able to provide 10 Amps for one hour. That same 10Ah battery being discharged at a C Rating of 0.5C will provide 5 Amps over two hours, and if discharged at a 2C Rate it will provide 20 Amps for 30 minutes. The C Rating of a battery is important to know as with the majority of batteries the available stored energy depends on the speed of the charge and discharge currents.

BATTERY C RATE CHART

The below chart shows the different battery C Rates along with their service times. It is important to know that even though discharging a battery at different C Rates should use the same calculations as an identical amount of energy, in reality there are likely to be some internal energy losses. At higher C Rates some of the energy can be lost and turned in to heat which can result in lowering the capacity by 5% or more.

HOW TO CALCULATE C RATING OF A BATTERY

A battery’s C Rating is defined by the rate of time in which it takes to charge or discharge. You can increase or decrease the C Rate and as a result this will affect the time it takes the battery to charge or discharge. The C Rate charge or discharge time changes in relation to the rating. 1C is equal to 60 minutes, 0.5C to 120 minutes and a 2C rating is equal to 30 minutes.

The formula is simple.

t = Time Cr = C Rate t = 1 / Cr (to view in hours) t = 60 minutes / Cr (to view in minutes)

2300mAh Battery
2300mAh / 1000 = 2.3A
0.5C x 2.3A = 1.15A available
1 / 0.5C = 2 hours
60 / 0.5C = 120 minutes

2300mAh Battery
2300mAh / 1000 = 2.3A
2C x 2.3A = 4.6A available
1 / 2C = 0.5 hours
60 / 2C = 30 minutes

2300mAh Battery
2300mAh / 1000 = 2.3A
30C x 2.3A = 69A available
60 / 30C = 2 minutes

You can see the 30C rate example on the datasheet for Power Sonic 26650 LiFePO4 power cell

You can use the formula below to calculate output current, power and energy of a battery based on its C rating.

Er = Rated energy (Ah) Cr = C Rate I = Current of charge or discharge (Amps) I = Cr * Er Cr = I / Er

Smaller batteries are commonly rated at the 1C rating, which is also know as the one-hour rate. For example if your battery is labelled 3000mAh at the one-hour rate, then the 1C rating is 3000mAh. You will generally find the C rate of your battery on it’s label and on the battery data sheet. Different battery chemistries will sometimes display different C rates, for instance lead acid batteries are generally rated at a very low discharge rate often 0.05C, or 20-hour rate. The chemistry and design of your battery will determine the maximum C rate of your battery, lithium batteries for instance can tolerate much higher discharging C Rates than other chemistries such as alkaline. If you cannot find the battery C rating on the label or data sheet we advise contact the battery manufacturer directly.

Capacity of lithium battery vs lead acid at various discharge currents

There are an increasing number of applications and devices on the market that require a high C Rate discharge battery. These include industrial and consumer applications like RC models, drones, robotics and vehicle jump starters. All these applications require a powerful energy burst in a short period of time.

Most jump starters can require up to 35C Rate discharge and in the RC industry there are high rate discharge batteries used up to 50C Rate! There are some batteries on the market that claim even higher C Rates based on maximum pulse discharge rates which require the battery to reach full discharge in just a few seconds. Most applications, however do not need such high C Rates.

If you need any help finding the right battery for your application please get in touch with one of the the Power Sonic application engineers.

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