Semiconductors/Variable Resistance

The drain current in a MOS transistor in linear region is given by following equations.

$IDS=\mu Cox{\frac {W}{L}}(VDS(VGS-VT)-{\frac {W}{L}}VDS^{2})$

So, for a transistor, which is in linear region, as the VDS decreases the significance of the VDS squared term slowly vanishes. For significantly small VDS, the current is proportional to VDS with the proportionality factor of

$GDS=\mu Cox{\frac {W}{L}}VDS(VGS-VT)$

The resistance is given by

$RDS={\frac {1}{\mu Cox{\frac {W}{L}})(VGS-VT)}}$

Thus the resistance is controlled by the VGS. This way, a variable resistor can be implemented by the transistor.