Q. How can a JFET be used as a voltage controlled resistor. Explain from drain characteristics?

The region to the left of the pinch off locus is referred to as the ohmic region or the voltage controlled region. In this region the JFET can actually be employed as a variable resistor whose resistance is controlled by the applied gate source voltage. Not in the characteristic shown below that the slope of each curve and therefore the resistance of the device between the drain and source for VDS < VP is a function applied voltage VGS. As VGS becomes more and more negative, the slope of each curve becomes more and more horizontal corresponding with an increase in resistance level. The following approximation will provide a good first approximation to the resistance level in terms of the applied voltage V_gs.

     r_D =  r₀ / (1-V_GS / V_P)²

where r₀ the resistance with V_GS = 0 V and r_D the resistance at a particular level of gate source voltage.
It is important to note that the depletion region is wider near the top of both p-type material. The reason for this is that the drain current flowing through the channel sets up a drain resistance that varies with the length of the channel. This phenomenon can be used for the making of a variable resistor.