The measurement of an unknown resistance $R$ is to be carried out using the Wheatstone bridge as given in the figure. Two students perform an experiment in two ways. The first students take $R_2=10 \mathrm{\Omega }$ and $R_1=5$$\mathrm{\Omega }$. The other student takes $R_2=1000 \mathrm{\Omega }$ and $R_1=500 \mathrm{\Omega }$. In the standard arm, both take $R_3=5 \mathrm{\Omega }$. Both find $R\mathit{=}\frac{{\mathit{R}}_{\mathit{2}}}{{\mathit{R}}_{\mathit{1}}}\mathit{,}\mathit{ }{R}_{\mathit{3}}=100 \mathrm{\Omega }$ within errors.