# Problem Statement A p-channel enhancement MOSFET has: - \( V_{t} = -.5\,V \) - \( K = .2\,mA/V^2 \) Assuming operation in the saturation region, **what value of \( V_{SG} \) is required for \( I_D = .8\,mA \)?** --- ## Solution For a p-channel MOSFET in saturation: \[ I_D = K (V_{SG} - |V_{t}|)^2 \] Given: - \( I_D = .8\,mA \) - \( K = .2\,mA/V^2 \) - \( |V_{t}| = .5\,V \) Plugging in: \[ .8 = .2 \cdot (V_{SG} - .5)^2 \] \[ \frac{.8}{.2} = (V_{SG} - .5)^2 \] \[ 4 = (V_{SG} - .5)^2 \] \[ V_{SG} - .5 = \pm 2 \] \[ V_{SG} = 2 + .5 = 2.5\,V \quad \text{or} \quad V_{SG} = -2 + .5 = -1.5\,V \] For a **p-channel MOSFET**, \( V_{SG} \) is usually **positive** (source is more positive than gate), so: \[ \boxed{V_{SG} = 2.5\,V} \] --- ### Final Answer \[ \boxed{V_{SG} = 2.5\,\text{V}} \] is required for \( I_D = .8\,\text{mA} \).