5. For a long channel \( n \)-MOSFET with \( V_{t}=1 \mathrm{~V} \), calculate the \( V_{g} \) required for an \( I_{d}\left(\right. \) sat.) of 0.1 mA and \( V_{d}( \) sat.) of 5 V . Calculate the small-signal output conductance, \( g \) and the transconductance, \( g_{m}\left(\right. \) sat. ) at \( V_{d}=10 \mathrm{~V} \). Sketch the cross section of this MOSFET and schematically show the inversion charge and depletion charge distributions for \( V_{d}=1 \mathrm{~V}, 5 \mathrm{~V} \) and 10 V . Recalculate the new \( I_{d} \) for \( V_{g}-V_{t}=3 \mathrm{~V} \) and \( V_{d}=4 \mathrm{~V} \).