$($a$)$ Study the circuit depicted in figure $7\mathrm{.}1,$ and explain $($in terms of KCL $)$ why the voltage labeled $Vx$ must be zero.

$($b$)$ In the Wheatstone bridge circuit of figure $7\mathrm{.}2$ select the values of $R_a$ and $R_b$ such that the bridge can measure $R_x$ in the range of $0-25.$

Figure $7\mathrm{.}2$

$($c$)$ As shown in figure $7\mathrm{.}2,$ the adjustable resistor has a linear taper with a maximum value of $150.$ If the resistance $R_x$ is found to be $22\mathrm{.}6,$ then analyze the circuit for the fraction of the full slider travel when the bridge is balanced.