Q.Given $I_D = 10$ mA and $V_{GS} = -1$ V, determine the value of $V_P$ if $I_{DSS} = 20$ mA.

Shockley's equation is the fundamental relation that gives the drain current of a JFET in its pinch-off (saturation) region:

Here $I_{DSS}$ is the drain-source saturation current (the maximum drain current, flowing when $V_{GS}=0$), $V_{GS}$ is the gate-to-source voltage, and $V_P$ is the pinch-off voltage. The squared bracket is why the transfer characteristic is a curve rather than a straight line.

The equation captures the two limiting cases neatly: when $V_{GS}=0$ the bracket equals 1, so $I_D = I_{DSS}$ (maximum current); and when $V_{GS}=V_P$ the bracket is zero, so $I_D = 0$ (pinch-off). For any bias in between, it predicts the drain current. …