Refer to the video below for the setting up of the apparatus. Why do you need a variable resistor (rheostat)? Without the variable resistor, you will have only one set of current I and potential difference V readings. Using the formula R = V/I, you are able to find the unknown resistor. But this method is not so accurate . Hence, to make it more accurate, we include a variable resistor to control the size of the current through the circuit. Thus having different readings of the potential difference V across the unknown resistor . Instead of just one set of readings of I and V, we now have about 5 sets. This allows us to plot a graph of V against I. By finding the gradient of the best fit line , we are able to find the resistance more accurately. [gradient = V / I = R, hence the gradient of V-I graph represents resistance R] For pure metallic conductor , like the fixed resistor R, it obeys the Ohm’s Law , hence it is an ohmic conductor. From the graph, the current I flowing the conductor is directly proportional to potential difference V across the conductor, provided physical conditions like temperature remains constant. [the graph is a straight line with constant gradient, and passes through the origin]

The variable resistor (rheostat) is a device to control the size of the current by adjusting the resistance on the variable resistor . Hence just device can be used to adjust the brightness of the bulb or the fan speed.