# Four resistance 40$\Omega$, 60 $\Omega$, 90$\Omega$ and 110$\Omega$ make the arms of a quadrilateral ABCD. Across AC is battery of emf 40V and internal resistance negligible. The potential difference across BD in V is_____________. Option: 1 2 Option: 2 4 Option: 3 6 Option: 4 8

$\begin{array}{l} \mathrm{i}_{1}=\frac{40}{40+60}=0.4 \\ \\ \mathrm{i}_{2}=\frac{40}{90+110}=\frac{1}{5} \\ \\ \mathrm{v}_{\mathrm{B}}+\mathrm{i}_{1}(40)-\mathrm{i}_{2}(90)=\mathrm{v}_{\mathrm{D}} \\ \\ \mathrm{v}_{\mathrm{B}}-\mathrm{v}_{\mathrm{D}}=\frac{1}{5}(90)-\frac{4}{10} \times 40 \\\\ \mathrm{v}_{\mathrm{B}}-\mathrm{v}_{\mathrm{D}}=18-16=2 \end{array}$

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