My car battery when fully charged operated the car lights and air conditioning for a few minutes (without the engine being on) before it was not powerful enough to operate the starter motor.
The garage applied a meter to the battery and told me that the capacity was about one third of what it should be.
How could the garage measure the capacity of the battery with one instantaneous meter reading?
Here is how.
That special meter contains a load resistor, which places a load on the battery roughly equal to that of a starter motor (big load!). When the meter is clipped onto the battery terminals, the battery voltage sags down as the battery struggles to feed power to the load resistor. The amount of voltage sag under load yields a rough estimate of the battery's storage capacity.
A battery with impaired capacity (because of sulfated plates, which is the main wearout mode of a lead-acid battery) will sag a lot. A battery in new condition will sag less.
Typically, voltage decreases as the battery discharges, so it is probably possible to assess the remaining energy of a battery by measuring the voltage. It is also plausible that the voltage (of a fully charged battery) decreases as the capacity decreases. However, I cannot be sure your garage is not trying to deceive you:-)
A simple circuit equivalent of a battery is a voltage source with a series resistor. For a fully charged, new battery the series resistance is relatively low. A lead-acid battery for a vehicle with a starter motor has to supply a high current for a short duration to the starter motor and the vehicle electronics.
A fully charged, relatively low capacity, nominally 12V, lead-acid battery for a small vehicle such as a motorcycle will have a similar, open circuit voltage as a larger capacity, 12V battery in a car, bus or truck. The simple equivalent circuit for the small capacity battery will have a higher series resistance. When a high current load such as a car starter motor is placed across the terminals of the small capacity battery the voltage across the internal series resistance will cause the terminal voltage of the battery to fall to a voltage too low for a vehicle to start.
For most of its service life, a car battery's storage capacity only falls by a relatively small amount and the equivalent series resistance only increases slowly. Once the lead-acid battery's storage capacity has fallen to 80% the rate of loss of storage capacity in use accelerates and manufacturer's consider the battery has entered an end-of-life phase and should be replaced. The open circuit, terminal voltage of a fully charged, end-of-life battery can still appear to be acceptable. The most significant change will be an increase in the internal series resisctance so that when a high current load is applied the terminal voltage will drop to an unacceptable value.
A manufacturer can vary the chemical composition of a lead-acid battery (e.g. replace antimony with calcium) and vary construction such that there are slight terminal voltage variations between nominally 12V batteries. The open circuit terminal voltage of a fully charged,lead-acid will typically fall very slowly with age but is not really a useful measure of the storage capacity.
For a quick and simple test at the garage it is not possible to directly measure the storage capacity. A charge/discharge cycle will provide the actual storage capacity of the battery but that could take hours. Therefore a garage tester uses the changes in internal series resistance to estimate the condition of the battery.
A simple tester applying a load equivalent to a starter motor to a battery can measure a decrease in terminal voltage and provide an estimate of battery capacity. Heavy duty leads and battery clamps are required for a high current load. The process of connecting and disconnecting a high current load can generate sparks. Lead-acid batteries can generate hydrogen and in a confined space this can create the risk of an explosion. Another problem is a garage can be required to test batteries from a small motorcycle to the largest truck and everything in between. Therefore a simple load to test a truck battery will not be appropriate for the smallest capacity batteries. High current/low resistance loads could be manually switched to test a range of batteries. If the battery is not charged the change in terminal voltage may incorrectly report a battery is defective. Historically this type of tester has been very cheap to manufacture, rugged in service and can provide a simple to interpret meter reading.
A high current load is not the only method of measuring the internal resistance of a battery. A battery impedance meter will use 1kHz or a similar frequency to directly measure the internal resistance. This does not require such a high current load on the battery and provides an accurate measurement of the equivalent, internal resistance of the battery. The impedance meter may report resistance in milleOhms or less likely for a garage report the conductance in Siemens.
Given the symptoms it is most likely that the battery has reached end-of-life and less likely there is a charging problem. Performance of a Lead-Acid battery is temperature dependent which is one contributor to vehicle starting problems in cold temperatures. Therefore testing in hot weather may indicate a battery is acceptable or marginal when it has reached end-of-life. The garage is most likely to replace the vehicle battery as their first attempt to correct the described symptoms.
From the symptoms the garage may have used a simple voltmeter to confirm the vehicle had been charging the battery and then declared the battery was dead. From the question it is not possible to determine which method (load, impedance, or voltmeter) has been employed by the garage. All these will provide a quick answer.
