While checking for a fast battery charger circuit

The IC LM338 is an outstanding device which can be used for unlimited number of potential electronic circuit applications. Basically the main function of this IC is voltage control and can also be wired for controlling currents through some simple modifications. Battery charger circuit applications are ideally suited with this IC and we are going to study one example circuits for making a 12 volt automatic battery charger circuit using the IC LM338.

Referring to the circuit diagram we see that the entire circuit is wired around the IC LM301, which forms the control circuit for executing the trip off actions. 

The IC LM338 is configured as the current controller and as the circuit breaker module. The whole operation can be analyzed trough the following points:

The IC LM 301 is wired as a comparator with its non inverting input clamped to a fixed reference point derived from a potential divider network made from R2 and R3.

The potential acquired from the junction of R3 and R4 is used for setting the output voltage of the IC LM338 to a level that’s a shade higher than the required charging voltage, to about 14 volts.

This voltage is fed to the battery under charger via the resistor R6 which is included here in the form of a current sensor.

The 500 Ohm resistor connected across the input and the output pins of the IC LM338 makes sure that even after the circuit is automatically switched OFF, the battery is trickle charged as long as it remains connected to the circuit output.

The start button is used to initiate the charging process after a partially discharged battery is connected to the output of the circuit.

R6 may be selected appropriately for acquiring different charging rates depending upon the battery AH.

Circuit Functioning Details (As Explained By +ElectronLover)

" As soon as the connected battery is charged fully, the potential at the inverting input of the opamp becomes higher than the set voltage at non-inverting input of the IC. This instantly switches the output of the opamp to logic low."

According to me:
V+ = VCC - 74mV
V- = VCC - Icharging x R6
VCC= Voltage on pin 7 of Opamp.
When The battery charges fully Icharging reduces. V- become greater than V+, output of the Opamp goes low, Turning on the PNP and LED.
Also,
R4 gets a ground connection through the diode. R4 becomes parallel to R1 reducing the effective resistance seen from the pin ADJ of LM338 to GND. 
Vout(LM338) = 1.2+1.2xReff/(R2+R3), Reff is the Resistance of pin ADJ to GND.

When the Reff reduces the output of LM338 reduces and inhibit charging.