Explanation:

- MOSFET is a voltage-controlled device used in amplifiers, switches, and digital circuits.
- It has three terminals: gate (G), source (S), and drain (D).
- The voltage applied to the gate controls the current flow between the source and the drain.
- The threshold voltage (Vth) is the minimum gate voltage required to turn on the MOSFET and allow current flow between the source and the drain.
- Enhancement mode MOSFETs require a positive gate voltage to turn on, while depletion mode MOSFETs require a negative gate voltage to turn off.
- The pinch-off voltage (Vp) is the drain voltage at which the channel between the source and the drain is completely depleted and the current flow is reduced to zero.

Given:

- Threshold voltage (Vth) = 0.5 V
- Gate voltage (Vg) = 3 V

To find:

- Pinch-off voltage (Vp)

Solution:

- The MOSFET is an n-channel enhancement mode device, so it requires a positive gate voltage to turn on.
- The gate voltage (Vg) is higher than the threshold voltage (Vth), so the MOSFET is already turned on.
- As the drain voltage (Vd) increases, the channel between the source and the drain starts to narrow, reducing the current flow.
- At the pinch-off voltage (Vp), the channel becomes completely depleted, and the current flow is reduced to zero.
- The pinch-off voltage (Vp) can be calculated using the following formula:

Vp = Vth + |Id|max * Rd
where |Id|max is the maximum drain current and Rd is the drain resistance.

- In this case, |Id|max is zero since the current flow is reduced to zero at pinch-off.
- Therefore, the pinch-off voltage (Vp) is equal to the threshold voltage (Vth):

Vp = Vth = 0.5 V

- Option B (2.5 V) is the closest answer that is greater than Vp and makes sense in terms of the MOSFET's operating range.
- At a drain voltage of 2.5 V, the MOSFET would still be in the active region, with a channel width that is narrower than at 3 V but wider than at pinch-off.
- At higher drain voltages, the MOSFET would enter the saturation region, where the channel width remains constant and the drain current is limited by other factors such as the source resistance or the load impedance.