(Solved): The op amp circuit shown below is intended to provide any gain between \( -10 ...

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The op amp circuit shown below is intended to provide any gain between \( -10 \) (when \( \mathrm{k}=0 \) ) and \( +10 \) (when \( \mathrm{k}=1 \) ) by adjusting the potentiometer. Let \( R_{1} \) and \( R_{2} \) have the scaled values, (a) Show that \[ \frac{V_{2}}{V_{1}}=\frac{r_{1}}{r_{1}+10 k}\left[\frac{-11}{1+\frac{10 k r_{1}}{r_{1}+10 k}}\right]+\frac{r_{2}}{r_{2}+10(1-k)}\left[1+\frac{11}{1+\frac{10 k r_{1}}{r_{1}+10 k}}\right] \text {, } \] (b) Determine expressions for \( r 1 \) and \( r 2 \), (c) For what value of \( \mathrm{k} \) is the gain 0 ?