Knowing how long a battery should last can help save you money and energy. The discharge rate affects the lifetime of a battery. Specifications and features of how electric circuits with battery sources let current flow are the basis for creating electronics and electronic-related equipment. The rate at which charge flows through a circuit depends on how quickly a battery source can send current through it based on its discharge rate.

## Calculating Discharge Rate

You can use Peukert's law to determine the discharge rate of a battery. Peukert's Law is

in which *H* is the rated discharge time in hours, *C* is the rated capacity of the discharge rate in amp-hours (also called the AH amp-hour rating), *I* is the discharge current in amps, *k* is the Peukert constant without dimensions and *t* is the actual discharge time.

The rated discharge time for a battery is what the battery manufacturers have rated as the discharge time for a battery. This number is usually given with the number of hours at which the rate was taken.

The Peukert constant generally ranges from 1.1 to 1.3. For Absorbent Glass Mat (AGM) batteries, the number is usually between 1.05 and 1.15. It can range from 1.1 to 1.25 for gel batteries, and it can generally be 1.2 to 1.6 for flooded batteries. BatteryStuff.com has a calculator for determining the Peukert constant. If you don't want to use it, you can make an estimate of the Peukert constant based on the design of your battery.

To use the calculator, you need to know the AH rating for the battery as well as the hour rating at which the AH rating was taken. You need two sets of these two ratings. The calculator also accounts for extreme temperatures at which the battery operates and the age of the battery. The online calculator then tells you the Peukert constant based off of these values.

The calculator also lets you tell it the current when connected to an electrical load so the calculator can determine capacity for the given electrical load as well as the runtime to keep a discharge level safely at 50%. With the variables of this equation in mind, you can rearrange the equation to get

^{} to get the product *It* as current times time, or the discharge rate. This is the new AH rating you can calculate.

## 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 *It* 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 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 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-magnanese 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 V _{avg}* for energy

*E* in watt-hours, capacity in amp-hours

*C* and

*V* average voltage of the discharge.

_{avg}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.

## Battery Discharge Calculator

Using a battery discharge calculator can give you a deeper understanding of how different battery materials affect discharge rate. Carbon-zinc, alkaline and lead acid batteries generally decrease in efficiency when they discharge too quickly. Calculating discharge rate lets you quantify this.

The discharge of a battery provides you with methods of calculating other values such as capacitance and the discharge rate constant. For a given charge given off by a battery, the battery's capacitance (not to be confused with capacity, as discussed earlier) *C* is given by *C = Q/V* for a given voltage V*.* The capacitance, measured in farads, measures the battery's ability to store charge*.*

A capacitor arranged in series with a resistor can let you calculate the product of capacitance and resistance of the circuit that gives you the time constant τ as τ = RC. The time constant of this circuit arrangement tells you the time it takes for the capacitor to consume about 46.8% of its charge when discharging through a circuit. The time constant is also the circuit's response to a constant voltage input so engineers frequently use the time constant as a cutoff frequency for a circuit

## Capacitor Charging and Discharging Applications

When a capacitor or battery charges or discharges, you can create many applications in electrical engineering. Flashlamps or flashtubes produce intense bursts of white light for short periods of time from a polarized electrolytic capacitor. These are capacitors that have a positively charged anode which oxidizes by forming an insulator metal as a means of storing and producing charge.

The light of the lamp comes from the lamp's electrodes connected to a capacitor with a large amount of voltage so they can be used for flash photography in cameras. These are typically made with a step up transformer and a rectifier. The gas in these lamps resist the electricity so the lamp won't conduct electricity until capacitor discharges.

Aside from straightforward batteries, the discharge rate finds use in capacitors of power conditioners. These conditioners protect electronics from surges in voltage and current work by eliminating electromagnetic interference (EMI) and radio-frequency interference (RFI). They do this through a system of a resistor and a capacitor in which the capacitor's rate of charging and discharging prevents voltage spikes from occurring.

References

- Batterystuff: Peukert’s Law | A Nerd’s Attempt to Explain Battery Capacity
- Battery University: https://batteryuniversity.com/learn/article/bu_503_how_to_calculate_battery_runtime
- Powerstream: How to calculate battery runtimes
- AllAboutCircuits: Capacitor Charge and Time Constant Calculator
- XenonFlashtubes: Trigger coil Transformers
- XenonFlashTubes: Misc Components
- PetaPixel: https://petapixel.com/2015/10/05/a-brief-history-of-the-camera-flash-from-explosive-powder-to-led-lights/
- Adrafruit learning: Power Capacity and Power Capability

Resources

Tips

- You will notice that both the rating of the battery and the rating of the device in the example were prefixed with "milli" which indicates 1/1000th. If both excluded this prefix, you could still follow the same prescription described above to perform the calculations. However, if one includes the "milli" prefix and the other does not, then you should multiply the one that does not include the prefix by 1,000 to make the calculations work out correctly.
- Most devices that use multiple batteries connect them in series to provide a higher voltage. Since the discharge rate depends only on the current drain, this has no effect on the calculations, and it is incorrect to simply add ratings from Step 1 of all the batteries together. In fact, you should use the battery with the lowest rating.
- On the other hand, you may find some devices that wire the batteries in parallel. In this case it would be appropriate to add the ratings of all the batteries together to provide the result used in Step 1. If you are not certain of whether your device has its batteries in parallel or series, you can find an excellent tutorial on that topic at Battery University (see Resources).

About the Author

S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.