An ideal battery of emf \(\varepsilon\) is connected across a potentiometer of total resistance \(R\). A sliding contact (wiper) is positioned at the midpoint, dividing the potentiometer into two equal sections, each of resistance \(R/2\). A load resistor of resistance \(R_L = R\) is then connected between the wiper and the bottom terminal of the potentiometer. What is the output voltage \(V_{\text{out}}\) across the load resistor, and how does \(V_{\text{out}}\) compare to the unloaded output voltage \(V_{\text{unloaded}}\) measured at the midpoint before the load resistor was attached?