Explanation

(a) Applying Kirchhoff’s law in mesh $ABCDA$
$- 10\left( i - i_{1} \right) - 10i_{2} + 20i_{1} = 0\ \Rightarrow 3i_{1} - i_{2} = i$ …(i)
And in mesh $BEFCB$
$- 20\left( i - i_{1} - i_{2} \right) + 10\left( i_{1} + i_{2} \right) + 10i_{2} = 0$
$\Rightarrow 3i_{1} + 4i_{2} = 2i$ …(ii)
From equation (i) and (ii)
$i_{1} = \frac{2i}{5},i_{2} = \frac{i}{5} \Rightarrow i_{AD} = \frac{2i}{5}$