What Wire Gauge and Conduit Size for 15a Cicruit Extension?
#14 is not adequate for a 175 foot, 50% circuit capacity load. Voltage drop is a function of resistance of the wire in series with the load. Extending a #14 circuit with lower resistance #12 is completely acceptable and does accomplish reducing the accumulated resistance that causes voltage loss on the extension.
5% is the total drop generally considered the maximum acceptable. Figure a distance to the gate of 100', add your 75' extension, you have 175', with an 7.5 amp load (a worm drive saw) you have a 3.5% loss just getting to the gate, then an additional 3% getting to your new receptacle. But if you reduce the resistance on the extension by using #12 you will get only about 1.5% loss on your extension, bringing you back to 5%. (Numbers get dramatically worse if you exceed the 50% circuit capacity that I used above.)
The 18&quot; cover requirement is adequate for most conditions, be aware it is 18&quot; of &quot;cover&quot;, meaning the conduit is to be below 18&quot; of material. Do an internet search for table 300.5 that could identify conditions that could change depth requirements.