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The cross section of a JFET is shown in the following figure. Let $V_{G}$ be $-2 \mathrm{~V}$ and let $V_{P}$ be the initial pinch-off voltage. If the width $\mathrm{W}$ is doubled (with other geometrical parameters and doping levels remaining the same), then the ratio between the mutual transconductances of the initial and the modified JFET is

1. $4$
2. $\frac{1}{2}\left(\frac{1-\sqrt{2 / V_{p}}}{1-\sqrt{1 /\left(2 V_{p}\right)}}\right)$
3. $\frac{1-\sqrt{2 / V_{p}}}{1-\sqrt{1 /\left(2 V_{p}\right)}}$
4. $\frac{1-\left(2 / \sqrt{V_{p}}\right)}{1-\left(1 /\left(2 \sqrt{V_{p}}\right)\right)}$