Ideal resistance of a variable resistor
Rheostat resistance too small: can't turn bulb off
Simulations to let you see the problems of trying to control a bulb using both high and low resistance variable resistors.GCSE Maths exam soon?
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If you connect a rheostat (variable resistor) in series with a bulb you'll probably notice it doesn't work very well at changing the brightness.
If the maximum resistance is about the same or smaller than the resistance of your bulb you'll find that you can't turn the bulb off completely.
Rheostat resistance too big: bulb is off most of the time
If the maximum resistance is much bigger than the resistance of the bulb there's a different problem. For most of the length of the rheostat the bulb is off and then at one end it changes very rapidly for very tiny changes in jockey position.
If you want to be able to turn the bulb completely off and use the full length of the rheostat you need to set the rheostat up as a potential divider.