# Answer on Electric Circuits Question for gabby

Question #15836

A 550-W space heater is designed for operation in Germany, where household electrical outlets supply 230V (rms) service. what is the power output of the heater when plugged into a 120-V (rms) electrical outlet in a house in the united states? ignore the effects of temperature on the heaters resistance.

Expert's answer

Let's find the current consumed by the heater in normal use:

P = UI ==> I = P/U = 550[W]/230[V] ≈ 2.39[A].

Let's find the resistance of a heater:

P = I²R ==> R = 550[W]/(2.39[A])² ≈ 96.29[Ω].

The current consumption when plugged into a 120-V electrical outlet will be

I = U/R = 120[V]/96.29[Ω] ≈ 1.25[A].

So, the power output of the heater when plugged into a 120-V electrical outlet will be

P = I²R = (1.25[A])² * 96.29[Ω] ≈ 150[W].

P = UI ==> I = P/U = 550[W]/230[V] ≈ 2.39[A].

Let's find the resistance of a heater:

P = I²R ==> R = 550[W]/(2.39[A])² ≈ 96.29[Ω].

The current consumption when plugged into a 120-V electrical outlet will be

I = U/R = 120[V]/96.29[Ω] ≈ 1.25[A].

So, the power output of the heater when plugged into a 120-V electrical outlet will be

P = I²R = (1.25[A])² * 96.29[Ω] ≈ 150[W].

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