Explanation:
The current Ids in a MOSFET remains fairly constant as Vds (drain-source voltage) increases. This is due to the fact that the MOSFET operates in the saturation region when Vds is sufficiently high.

Reasons why Ids remains fairly constant as Vds increases:
- Saturation Region: In the saturation region of a MOSFET, the current Ids remains fairly constant with respect to changes in Vds. This is because the MOSFET is already fully conducting in this region, and further increases in Vds do not significantly affect the current flow.
- Negligible Channel Length Modulation: In MOSFETs, channel length modulation effects are typically negligible in comparison to other factors. This means that changes in Vds do not lead to significant variations in the channel length, and hence the current remains fairly constant.
- Constant Current Source: In the saturation region, the MOSFET can be modeled as a constant current source. This means that the current flowing through the device is largely independent of changes in Vds, resulting in a fairly constant current.
- Ohmic Region: In the ohmic region of a MOSFET, where Vds is low, the current may vary with changes in Vds. However, once the device enters the saturation region, the current remains fairly constant even as Vds increases.
In conclusion, the current Ids in a MOSFET remains fairly constant as Vds increases due to the device operating in the saturation region, negligible channel length modulation effects, and the MOSFET behaving like a constant current source in this region.