A student sets up the Wheatstone bridge circuit shown in the figure to measure an unknown resistance R_x , which is known to be approximately 50 . The bridge is balanced by adjusting the variable standard resistance R_s . To ensure the maximum sensitivity of the bridge (and hence the most precise measurement of R_x ), which of the following pairs of values should be chosen for the ratio arms R₁ and R₂ ?

Step-by-step solution

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 , the standard resistance R_s will also be adjusted to approximately 50 to achieve balance if the ratio arms are equal. To ensure maximum sensitivity, the ratio arms R₁ and R₂ shou