A student sets up the Wheatstone bridge circuit shown in the figure...

For a Wheatstone bridge, the sensitivity is defined as the deflection of the galvanometer per unit fractional change in the unknown resistance. The bridge is most sensitive when the resistances of all four of its arms are of the same order of magnitude (i.e., approximately equal).

Given that the unknown resistance $R_x$ is approximately $50\ \Omega$, the standard resistance $R_s$ will also be adjusted to approximately $50\ \Omega$ to achieve balance if the ratio arms are equal.

To ensure maximum sensitivity, the ratio arms $R_1$ and $R_2$ should also be chosen to be approximately equal to $R_x$.

Therefore, choosing $R_1 = 50\ \Omega$ and $R_2 = 50\ \Omega$ makes all four arms of the bridge approximately equal ($R_1 \approx R_2 \approx R_x \approx R_s \approx 50\ \Omega$), which provides the most precise measurement.

Answer: $R_1 = 50\ \Omega$, $R_2 = 50\ \Omega$