Ac power

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Hoping someone here can give me a hand with an electrical engineering question:

I've replaced the cooling fan in our bosch oven with an aftermarket one (oem ones are £150, this one fits and works and was £17). The new one is significantly more powerful and therefore noisier, than the original and I'd like to stick something in series with it to slow it down.

I've calculated it as though it's dc and assumed that everything.behaves like a resistor, as that's the only way I know, and I am hoping that some kind soul can tell me if what I've worked out is valid.

 

Right:

Fan is 23w and 230v ac. I'm assuming that a voltage drop across it of about a third will do the job, so I'm proposing putting a lightbulb in series with it as a resistor.

 

For the fan, using p=vi then v=ir, I calculate that it has a resistance of 2300ohms.

 

Given that I want a third of the voltage to be taken by a resistor (the bulb) I need a bulb with a resistance of about 1000ohms. I've calculated that a bulb rated at 230v and 60w will have a resistance of 881ohms, which should do the job nicely.

 

In this application it'd only be getting about 70v, so should last forever, the fan would take the other 160v and work nice and quietly.

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I've actually revived the old fan with a combo of wd40 and 3in1 oil (bearings had seized), and it's now Back in and working fine. I'd still be interested in the answer though, if anyone knows.