In the given circuit the current $I_1$ is .............. $A$
Diffcult
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(b) The circuit can be simplified as follows
Applying $KCL$ at junction $A$
${i_3} = {i_1} + {i_2}$.….$(i)$
Applying Kirchoff’s voltage law for the loop $ABCDA$
$ - 30{i_1} - 40{i_3} + 40 = 0$
$ \Rightarrow \,\,\,\,\,\, - 30{i_1} - 40({i_1} + {i_2}) + 40 = 0$
$ \Rightarrow \,\,\,\,\,\,\,7{i_1} + 4{i_2} = 4$ .….$(ii)$
Applying Kirchoff’s voltage law for the loop $ADEFA.$
$ - 40{i_2} - 40{i_3} + 80 + 40 = 0$
$ \Rightarrow \,\,\,\,\, - 40{i_2} - 40({i_1} + {i_2}) = - 120$
$ \Rightarrow \,\,\,\,\,\,{i_1} + 2{i_2} = 3\,$…….$(iii)$
On solving equation $(ii)$ and $(iii)$ ${i_1} = - 0.4\,A$.
Applying $KCL$ at junction $A$
${i_3} = {i_1} + {i_2}$.….$(i)$
Applying Kirchoff’s voltage law for the loop $ABCDA$
$ - 30{i_1} - 40{i_3} + 40 = 0$
$ \Rightarrow \,\,\,\,\,\, - 30{i_1} - 40({i_1} + {i_2}) + 40 = 0$
$ \Rightarrow \,\,\,\,\,\,\,7{i_1} + 4{i_2} = 4$ .….$(ii)$
Applying Kirchoff’s voltage law for the loop $ADEFA.$
$ - 40{i_2} - 40{i_3} + 80 + 40 = 0$
$ \Rightarrow \,\,\,\,\, - 40{i_2} - 40({i_1} + {i_2}) = - 120$
$ \Rightarrow \,\,\,\,\,\,{i_1} + 2{i_2} = 3\,$…….$(iii)$
On solving equation $(ii)$ and $(iii)$ ${i_1} = - 0.4\,A$.
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