The correct answer is: B. Vds > Vgs
The channel pinches off when the drain-to-source voltage (Vds) exceeds the gate-to-source voltage (Vgs). This is because the drain-to-source voltage creates an electric field that opposes the flow of current through the channel. When the drain-to-source voltage is high enough, the electric field is strong enough to completely stop the flow of current, and the channel pinches off.
Option A is incorrect because the gate-to-source voltage must be greater than the threshold voltage (Vth) in order to turn on the transistor. However, once the transistor is turned on, the gate-to-source voltage does not affect the channel pinch-off.
Option C is incorrect because the drain-to-source voltage must be greater than the gate-to-source voltage in order to pinch off the channel.
Option D is incorrect because the gate-to-source voltage must be greater than the threshold voltage (Vth) in order to turn on the transistor. However, once the transistor is turned on, the gate-to-source voltage does not affect the channel pinch-off.