Soft Start Circuit
Where, VC1 is the voltage across capacitor, VBE is base to emitter voltage and 1.25 is the minimum output voltage of the LM317.
As the voltage across capacitor C2 increases, Vout rises at the same rate and reaches to the desired output voltage set according to the resistor’s value. Hence, as the output voltage reaches to the desired value the transistor turns off.
So, as we start the power supply, the bulb light starts getting brighter as per the voltage across it. So this circuit prevents the sudden rush of current into the circuit, hence prevents the device from getting damaged.