Current through wire $XY$ of circuit shown is ................ $A$
Medium
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$ - \,{i_1} + 0 \times {i_{xy}} + 3{i_2} = 0$ i.e. ${i_1} = 3{i_2}$ ...... $(i)$
Also $ - 2({I_1} - {I_{xy}}) + 4({I_2} + {I_{xy}}) = 0$
i.e. $2{I_1} - 4{I_2} = 6{I_{xy}}$ .... $(ii)$
Also ${V_{AB}} - 1 \times {i_1} - 2({i_1} - {i_{xy}}) = 0$ $\Rightarrow $ $50 = {i_1} + 2({i_1} - {i_{xy}})$
$ = 3{I_1} - 2{I_{xy}}$ .... $(iii)$
Solving $(i)$, $(ii)$ and $(iii)$, ${i_{xy}} = 2\,A$
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