Calculating Power of Outdoor Heater: A Puzzling Problem

[varyvod001]

Homework Statement

An outdoor heater has a resistance of 50 ohms and operates at 275 V. A transformer connected to a 120-V source supplies electricity to the heater. What is the power used by the transformer?

Homework Equations

P = V^2/R

The Attempt at a Solution

I plugged in the values V and R from the heater and calculated to get 1512.5 W. This is, coincidentally, the answer on my answer key, but I don't understand why...Why does calculating the power of the object give me the power of the heater and where does the 120-V part come in? :/

 

[Martinet]

Power is given by P = VI.

V, voltage, is energy per charge (Joules per coulomb)
I, current, is charge per time (Coulombs per second)

From this we can see that if we increase the voltage, the overall energy output will increase.

We can also see that if we increase the current, the same will happen. This is because there are more charges at a given voltage, therefore more energy.

Now we know P = IV. So where does V^2/R come from?

Ohm's law: V = IR.
When we rearrange, we get I = V / R.

Think about I = V / R and P = VI.

See what you come up with.

EDIT: Having read TSny's post and then yours again I realized I misinterpreted your question. I'll leave what I wrote here though in case it's useful.

 

[TSny]

varyvod001,

Not sure what "object" you are referring to when you say that you calculated the power of the "object". Seems to me you calculated the power used by the heater. Note that the question asks for the power used by the transformer.

The power used by the transformer is the power input to the transformer at 120 V. The transformer changes the input voltage of 120 V to the output voltage of 275 V. The power output by the transformer is the power used by the heater (which you have calculated).

So, you need to determine how the power that is input to a transformer is related to the power that is output by the transformer. Did you study this? The answer is pretty simple

 

[varyvod001]

I understand why the particular equation works in coming up with power. But I don't understand why using the resistance and voltage of the heater worked in calculating the power of the transformer. :)
Edit: So I calculated the output...And it works because the power input and output have to be the same, then?
I studied it...but I didn't really absorb a lot yet. :P

 

[TSny]

Yes, for an ideal transformer, the power input equals the power output. (For a real transformer there is some loss of power to internal heating. But real transformers can be close to ideal.)

 

[varyvod001]

Oh, okay...Makes sense now! Thank you very very very much! :D