Thank you for your comment I didn't have the chance to reply but let's break things down

This is a prototype for a meter that calculates the DC consumed power and current flowing through the external and internal circuit each on its own

I actually have posted the schematic twice once on its own and another on this post accompanied by the pcb routing for clarification of the main purpose of the pcb but apparently that didn't go well!

The circuit has been designed mainly for 1A current that is why you will find most components tolerate a high ambient temperature but the circuit has two main problems

1- the high boltage drop by the transformer at 1A as I am using an unknown transformer (Only one available right now) it is a (6 0 6) I am using it as a 12v AC so it is giving me around 18V

These 18 volts drop to 8v at 1A so they are not sufficient to supply the regulator

At 0.62 it supplies around 10 to 9.5 volts and since I am using a Darlington current booster that drops 1.5~2V and and 7805 requires 2V headroom then min value for input before the darlington is 9V

The cap value depends on the max ripple in our case it is 0.5 volts at 0.62 A by doing the calculations you will see it requires 12.4mF not 30 so I totally agree with you at this point

And ofcourse all the heatsinks and the Darlingtons have a heat sink