# Capacity (galvanic cell)

The capacity of a battery or an accumulator - hereinafter referred to simply as "battery" - indicates the amount of electrical charge that a battery can deliver or store according to the manufacturer's specifications. It is given: ${\ displaystyle Q}$

or

• as reserve capacity  C r, n in minutes (min); then, strictly speaking, it is the reciprocal of the C-factor, see u .

The capacity of a battery in the above sense must not be confused with the electrical capacity of a capacitor (batteries also have an electrical capacity), which is  specified in ampere-seconds per volt (As / V) or the unit Farad (F).

## General

The capacity of a battery that can be drawn depends on the course of discharge, i.e. the discharge current, the end-of- discharge voltage (the voltage at which the discharge is ended) and the degree of discharge . There are different types of discharge:

Depending on the course of discharge, the accumulator has a different capacity. In a meaningful specification of the nominal capacity, both the discharge current and the end-of-discharge voltage must therefore be given.

In general, the available capacity of a battery decreases with increasing discharge current. This effect is described by the Peukert equation . One of the reasons for this is the increasing voltage drop across the internal resistance of the battery, which causes the output voltage to drop accordingly so that the end-of-discharge voltage is reached earlier. In addition to the internal resistance, the limited speed of the electrochemical processes and charge transport processes in the battery is also responsible for its decreasing capacity with increased discharge current.

However, if the current consumption is reduced to the level of a normal discharge after an initial rapid discharge, practically the same amount of current can be withdrawn as with a normal discharge from the beginning. In the case of accumulators, such an operation, in which the current consumption is reduced as the battery charge drops, can only be implemented in a few cases.

To quantify the useful life of accumulators, when charging z. T. type-specific charging method used. The charging process itself is controlled by a charge controller.

The way in which several batteries are interconnected has an impact on the maximum amount of charge that can be drawn (capacity) and the electrical voltage available : when connected in series, the voltages of the individual batteries add up , whereas when connected in parallel, the amounts of charge add up .

## Acceptance during use

In the case of accumulators, the capacity decreases over time due to chemical reactions ( aging ) even when used properly . This is also known as degradation .

On the one hand, the charging and discharging processes on the electrodes lead to (only partially reversible) electrochemical processes that prevent full charging or discharging:

On the other hand, usage and service life usually have conflicting requirements. While the load capacity at higher temperatures due to better electron mobility increases, this leads to the higher reactivity of the electrode materials also decreasing life and capacity.

According to the wear level , the wear and tear of the battery, the charging capacity and thus the energy density decrease over the course of use . The service life of accumulators indicates the number of charge-discharge cycles after which the accumulator only has a certain charge capacity (generally 80% of the nominal capacity). The standards DIN 43539 Part 5 and IEC 896 Part 2 specify various methods and guide values for this.

The no-load voltage can serve as an indication of the remaining quality of an accumulator, which also decreases in the course of its service life when the accumulator is fully charged.

## C factor

### general description

The C-factor ( english C factor ), and C-rate ( English rate C ), is a colloquial quantification for charging and discharging of batteries. For example, it can be used to specify the maximum permissible charge and discharge currents, depending on the nominal capacity. In the opposite case, the factor is also used to specify the battery capacity as a function of the discharge current.

The C-factor is defined as the quotient of this current and the capacity of the accumulator: ${\ displaystyle C _ {\ text {N}}}$

${\ displaystyle C = {\ frac {I _ {\ text {max}}} {C _ {\ text {N}}}}}$

The dimension of the C-factor is:

${\ displaystyle [C] = \ mathrm {{\ frac {Electricity} {Charge}} = {\ frac {1} {Time}}}}$

The associated SI unit is therefore s −1 . In practice, however, is indicated almost exclusively in . ${\ displaystyle {\ tfrac {\ mathrm {A}} {\ mathrm {Ah}}} = \ mathrm {h} ^ {- 1}}$

The C-factor indicates the reciprocal value of the time for which a battery of the stated capacity can be discharged with the maximum discharge current.

The capacity of an accumulator is often much lower with very high current consumption (e.g. starter) than with low currents (e.g. electrical clock). For the discharge current-dependent capacity (see also Peukert equation ), these time-dependent specifications have become established. The capacity indicates the amount of charge available if the battery is discharged within 20 hours with a steady discharge current up to the final discharge voltage. For example, when calculating the maximum flight time of a drone, the C 0.5 or C 1 capacity of a battery delivers significantly more realistic values ​​than the C 20 value. ${\ displaystyle C_ {20}}$

If you multiply the resulting nominal capacity (also referred to as K 20 in this context ) by the nominal voltage ( unit of measurement : volt ), the result is the energy content (unit of measurement:  watt-hour ): ${\ displaystyle U _ {\ text {nenn}}}$ ${\ displaystyle E}$

${\ displaystyle E = C_ {20} \ cdot U _ {\ text {nenn}}}$

### Examples

The usual but formally incorrect notation "The maximum discharge current is 15 C." means:

With a capacity

${\ displaystyle C _ {\ text {N}} = 3 \, \ mathrm {Ah}}$

and:

${\ displaystyle I _ {\ text {max}} = C \ cdot C _ {\ text {N}} = 15 \, \ mathrm {h ^ {- 1}} \ cdot 3 \, \ mathrm {Ah} = 45 \ , \ mathrm {A},}$

the maximum discharge current of the battery is 45 A. Accordingly, the specification "charging current 2 C" for this cell means that it should be charged with a maximum of 6 A.

## Individual evidence

1. DIN EN 60095-1 Lead starter batteries - Part 1: General requirements and tests (Jan 1995)
2. Konrad Reif: Batteries, vehicle electrical systems and networking . Vieweg + Teubner, 2010, ISBN 978-3-8348-1310-7 , pp. 57 .