power and domestic electricity

Question

A hair dryer has two settings,600W and 1200W.At which setting do you expect the resistance of the heating element to be higher?

600 or 1200 W?

Answer 1

Let the Voltage be V
R be the resistance

　　　　　V^2
600W =　-------
　　　　　R1

　　　V^2
R1=　---------
　　　600

So the resistance of the heating element in 600W is V^2/600

　　　　　　V^2
1200W=　-------------
　　　　　　R2

　　　　V^2
R2=　------------
　　　1200

So the resistance of the heating element in 1200W is V^2/1200

R1　　　　2
-----　=　----------
R2　　　　１

Therefore the resistance of heating element of 600W is higher.