$3\mathrm{.}7.$ To eliminate possible bending effect due to eccentric loading, to eliminate effect due to temperature change, and to increase the circuit sensitivity$,$ four gages are mounted on a tensile specimen, as shown in Fig. P$3\mathrm{.}7.$ Determine the positions of the four gages in the bridge and derive an expression to relate the bridge output $E$ with the axial strain $lo{n}_a($a$)$ if a half bridge is to be used, and $($b$)$ if a full bridge is employed. Assume that a fixed voltage $V$ is applied to the bridge. The gage resistance, Poisson's ratio, and gage factor are $R_g,,$ and $G_f,$ respectively.