# Semiconductors/Variable Resistance

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

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

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

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

The resistance is given by

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

Thus the resistance is controlled by the VGS. In this ways a voltage variable resistor can be implemented bu the transistor.