If your power source is 120 V then 8000/120 = 66.7 Amps. If operated at 240 V then it is 33.3 Amps. In the first case you would need 3 AWG and in the second 8 AWG.
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For an 8 kW heater, you would typically use 10-gauge wire with a 30 amp breaker. Always consult the manufacturer's specifications and local electrical codes to ensure proper sizing and installation.
The formula you are looking for is I = W/E.
For a 13.8 kW electric heater at 208 volts, you would need a 3-phase circuit with a minimum of a 50-amp breaker to handle the load safely. This calculation is done by dividing the power (13,800 watts) by the voltage (208 volts) and then dividing by the square root of 3 (since it's a 3-phase system).
The formula you are looking for is I = W/E, Amps = Watts/Volts. Amps = 5000/230 =21.7 amps. The wire size to run this heater would be a #10 copper conductor. The supply breaker would be a two pole 30 amp breaker.
A 3 kW immersion heater circuit should be provided with a dedicated 15 Amp circuit that is protected by a 15 Amp circuit breaker and wired with appropriately sized cables (typically 14 AWG for residential wiring in the US). Additionally, a Ground Fault Circuit Interrupter (GFCI) protection may be required for safety.
The heater element is a coiled wire resistor that draws enough current to supply the intended amount of power, which might be 1.5 - 3 kW. Quickly the temperature of the wire rises until it reaches an equlibrium where the heat power conducted away by convection is the same as that draw from the power supply.