The transconductance ($g_m$) of a MOSFET depends on the gate-source voltage ($V_{gs}$) for a given drain bias. The general behavior of $g_m$ with respect to $V_{gs}$ is as follows:

1. In the subthreshold region, when $V_{gs}$ is low, $g_m$ is very small or near zero.
2. In the linear region, as $V_{gs}$ increases, $g_m$ increases sharply.
3. In the saturation region, $g_m$ reaches a peak and then starts to decrease as $V_{gs}$ continues to increase due to short-channel effects.

From the given options:

• The first graph shows a rise in $g_m$, reaching a peak, and then a drop-off, which is characteristic of MOSFET behavior when $g_m$ is plotted against $V_{gs}$ for a fixed drain bias.

Thus, the first graph best describes the variation of transconductance $g_m$ with gate voltage $V_g$ for a fixed drain bias in a MOSFET.

Would you like a more detailed explanation, or do you have any further questions?

Here are five related questions to explore:

1. What factors influence the peak of the transconductance $g_m$ in a MOSFET?
2. How does the channel length of a MOSFET affect the transconductance?
3. What is the role of threshold voltage in the behavior of $g_m$ vs. $V_{gs}$?
4. How does temperature impact MOSFET transconductance?
5. What is the difference between $g_m$ in long-channel and short-channel MOSFETs?

Tip: Transconductance $g_m$ is proportional to the derivative of drain current with respect to gate voltage, making it a key parameter for MOSFET amplifier performance.