Find the currents flowing through the branches AB and BC in the network shown.

Using Kirchhoff's voltage rule. In closed loop ABMNA: $\displaystyle -5 I_{1}+10\left(I-I_{1}\right)-5=0$ ……………………… ($\displaystyle 1$) In closed loop ACDNA: $\displaystyle -5 I-20 I+10-5-5 I_{1}=0$ ……………………….. ($\displaystyle 2$) Solving eq ($\displaystyle 1$) and ($\displaystyle 2$): $\displaystyle I_{1}=-\frac{3}{17} \mathrm{~A}$ and $\displaystyle I=\frac{4}{17} \mathrm{~A}$ Magnitude of current in arm AB $\displaystyle =\frac{3}{17} \mathrm{~A}$ Magnitude of current in arm BC $\displaystyle =\frac{4}{17} \mathrm{~A}$