Consider the adjustable gain difference amplifier in Figure P9.66. Variable resistor \(R_{V}\) is used to vary the gain. Show that the output voltage \(v_{O}\), as a function of \(v_{I 1}\) and \(v_{I 2}\), is given by

\[v_{O}=\frac{2 R_{2}}{R_{1}}\left(1+\frac{R_{2}}{R_{V}}\right)\left(v_{I 2}-v_{I 1}\right)\]

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