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A #3 copper conductor with an insulation factor of 90 degrees C is rated at 115 amps. Even though the panel is rated at a higher amperage it is the main breaker that governs the wire size.
For a 100 Amp breaker panel it would be 2 AWG. For 150 Amps it would require 2/0 (2 ought) aluminum wire.
A 200 amp service panel with a 60 amp sub-panel.
Yes you do. The detached garage will either be fed with a single circuit or a sub panel. The wire feeding the garage will need to be protected and that is the purpose of the breaker (disconnect). The breaker size will be determined by the size of the wire that is used on this circuit.
AWG # 3/0 copper.
Assuming you are referring to a 240 volt residential hot water heater you will need to install 10/2 NM cable (Romex) with ground from the service panel to the water heater wired to a 30 amp circuit breaker in the service panel. If you cannot see the water heater from the service panel you will need to install a service disconnect at the water heater.
Look to see if the 30 amp panel is fed with a two wire or a three wire. If it is a two wire then you are out of luck. If the panel is fed with a three wire then the panel should have the neutral terminated in the panel. It is this neutral that you need for 120 volt connections. You didn't state how many panel slots there are in the panel. If you are able install a 15 amp breaker into the panel and connect the wires going to the load. The black wire will go to the breaker and the white wire will go to the neutral bar in the panel.
You have two options, one is a complete service change. The average house service these days is 200 amps 42 circuits. The second option is to install a sub panel off the existing service. Depending on how many circuits you need will govern the size the sub panel. Here is where it gets tricky. Two side by side single pole breakers or one two pole breaker will have to be removed from the original service panel and replaced with a new two pole breaker. The size of this breaker will be governed by the total load of the new sub panel. The wire from the new sub panel to the two pole breaker is also governed by the load of the sub panel. As an electrician I would recommend that you not do it yourself but get a qualified electrician to do it for you. He would (should) take a permit out for the job and get it inspected.
A #3 copper conductor with an insulation factor of 90 degrees C is rated at 115 amps. Even though the panel is rated at a higher amperage it is the main breaker that governs the wire size.
When installing a circuit breaker, you size the breaker based on the wire size. The breaker should be matched to the ampacity of the wire to ensure proper protection against overloads and short circuits. The device being controlled by the breaker is not a determining factor in sizing the breaker.
#6 3 conducter
For a 100 Amp breaker panel it would be 2 AWG. For 150 Amps it would require 2/0 (2 ought) aluminum wire.
The wire size used in a service entrance distribution panel is governed by the size of the services over current device. The larger the service, the larger the fault current could be, the larger the ground wire to carry the fault current to ground. If the largest service conductor carries 100 amps use a #8, 200 amps - #6, 400 amps - #3, 600 amps - #1, 800 amps - 1/0 and over 800 amps - 2/0 for the ground wire. <<>> Golden Valley Electric Assoc. in Alaska requires #4AWG copper wire for a ground from the breaker box to earth ground rod. The same goes from the service entrance panel on the pole.
A 200 amp service panel with a 60 amp sub-panel.
Copper SE cable gauge 00 from the meter socket to the breaker panel for a 200A service. Then 8, 10, 12, and 14 gauge wire depending on the load.
I assume you mean you are wiring a 220 volt circuit. You will install a 220 volt double pole breaker of the correct size for the circuit. An example would be for an electric dryer that requires a 30 amp double pole breaker wired with 10/3 wire. You connect the Red & Black wires to the breaker. One on each screw. You now connect the White wire to the neutral bus bar in the service panel. Then connect the bare copper ground wire to the ground bus bar in the service panel. At the dryer outlet connect the black & red to the hot screws, white to the neutral, and ground to ground. They will be labeled on the back of the outlet.
A 200 amp service panel will require a # 4 bare copper ground wire.