Explanation:
The current distribution is shown in the figure. The potential difference across \(ABD\) is
\(10 - 2I - 3(I - {I_1}) - 3(I - {I_1}) = 0\)
\(10 = 8I - 6{I_1}\,\,\,\,\,\,\,\,\,\,(1)\)

Potential difference across \(ABC\) is
\(10 - 2I - 2{I_1} = 0\)
\(2I + 2{I_1} = 10\,\,\,\,\,\,\,\,\,\,(2)\)
From eq’s (1) and (2),
\({I_1} = \frac{{15}}{7}A,\;I = \frac{{20}}{7}A \Rightarrow I - {I_1} = \frac{5}{7}A\)