I have an inkbird ITC 308 wifi. And accidentally overloaded it. More than 10A. Everything seems to be working normally but I am not getting any voltage on either socket. What breaks when overloaded and what can I replace to get it working again?
Sorry, the maximum current supported by the ITC-308-WIFI socket is 10A. If it exceeds the limit, its relay may be damaged and cause output failure. If it is damaged, it is difficult to repair 
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You blew the rely contacts.
In order to carry a load even close to 10 amps you need to use the InkBird 308 to drive a power relay.
The output of the InkBird goes to the field wires of an auxiliary relay rated at 20 to 30 amps
Use that relay to control the heavy load.
I used a similar layout in my garage where the inkbird 308 drives a 110v auxiliary controller relay and
the auxiliary relay then controls the 220v line to feed a 5000w electrical heater. My auxiliary relay is a double pole single throw controller rated at 40 amps and my electrical heater draws about 28 amps … SAFETY MARGIN.
You might be able to open your 308 and replace the relay but for time, effort, safety and the cost of a replacement miniature relay … It Just Ain’t Worth It.
Buy a new 308 and use it as a driver.
The relay suggested will handle up to 40 amp and up to 330vac.
You may Google … AD-PR40-2C-120A
Or look at this site : https://www.automationdirect.com/adc/shopping/catalog/relays_-z-_timers/electro-mechanical_relays/ad-pr40-2c-120a?gad_source=1&gad_campaignid=18010732041&gclid=EAIaIQobChMIgLjU3dzdjQMVPGdHAR1bHxfbEAQYBSABEgKSL_D_BwE
Using this concept you may power most come equipment.