That's not really true. A discharged 12 V lead acid has a higher impedance than a charged unit due to the reduction in the specific grav. of the electrolyte. Therefore it self limits current.
That circuit depends on the battery Ah rating being small....ergo a relatively high impedance.
My statement is true; yours does not apply to 95% of the lead-acid battery charging process!
If you are discharging a lead-acid battery to where its impedance increases substantially, you are discharging it
much too deeply! The charge acceptance rate (charging current) of a lead-acid battery that is discharged to ~ 5% to 80% (95% to 10% charge remaining) MUST be limited! If not, you will either overheat the transformer, blow up the rectifiers, or overheat the battery.
Besides, even if the battery is over-discharged to where it should not go, its charge-acceptance rate might be low initially, but as soon as the S.G. comes up, it will accept very high charging (damaging) charging currents. At least, the LM317 circuit Mosaic linked to has built-in current limiting, but it does not rise to some other requirements for a good circuit mentioned below:
The circuit posted by Colin has no current limiting other than what
MAY be intrinsic in the wall-wart. It is an
extremely poor lead-acid battery charger.
1. No current-limiting (likely to blow-up or overheat the wall-wart)
2. Very primitive voltage regulation (using Vbe of transistor, which has very soft knee)
3. Extremely temperature sensitive for ambient temperature changes (Vbe of transistor is very temperature dependent)
4. No hysteresis. It will constantly cycle on/off as it approaches the set point. (as the OP has found out)
5. No attempt to do anything but cut-off the charger. Six-cell Sealed lead-acid (and flooded ones) requires one voltage to reach full-charge (14.5 to 14.8V) , and a different float voltage (~13.0 to 13.6V).
What voltage would you set the cutoff voltage of this simplistic charger to? If you say 13.5V, then the battery is only ~60% charged the first time that voltage is reached. If you say 14.5V, then this charger will turn back on after the battery drops a few mV, effectively holding the battery at too high a voltage for too long.!
Such a simplistic charger cannot do the job, and depending on how it is set up, will either
damage the battery by chronically undercharging it, or damage it by chronically overcharging it. Put another way, there is no single voltage setting of the trimpot that will not ultimately damage the battery it is connected to.