Question $2$: MOS, solve

Assume our usual nMOS model where:

Ohmic region

$I_D=k{V}_{DS}(V_{GS}-V_{TH})$

when $I_D=k(V_{GS}-V_{TH}{)}^2{V}_{DS}{V}_{GS}-V_{TH}{V}_{TH}=1V,V_{DD}=15V{R}_D=250I_D-V_{DS}k{V}_{GS}{V}_{DS}=5Vk=m\frac{A}{V^2}{V}_{GS}=V_{DS}$

Active region

$I_D=k(V_{GS}-V_{TH}{)}^2$

when

$V_{DS}{V}_{GS}-V_{TH}$

Consider the following circuit and the family $ofIV$ characteristic curves PLUS the load line $of$ the biasing circuit.

You are given that $V_{TH}=1V,V_{DD}=15V,$ and $R_D=250.$

Use the $I_D-V_{DS}$ characteristics $to$ find the transitor parameter $k$ and the value $of{V}_{GS}$ that produces $V_{DS}=5V.$

$k=$

$m\frac{A}{V^2}$

$V_{GS}=$

number $(2$ significant figures$)$

$V$