Find the value of current i_1 for the circuit | vedclass

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(B) Applying Kirchhoff's junction law at node $c$:$i_1 + i_2 = i_3$  --- $(i)$Applying Kirchhoff's loop law in loop $abcda$:$10.0 - (6.0)i_1 - (2.0)i_

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$2$

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(B) Applying Kirchhoff's junction law at node $c$:$i_1 + i_2 = i_3$  --- $(i)$Applying Kirchhoff's loop law in loop $abcda$:$10.0 - (6.0)i_1 - (2.0)i_3 = 0$$6.0i_1 + 2.0i_3 = 10.0$  --- $(ii)$Applying Kirchhoff's loop law in loop $befcb$:$-14.0 - 10.0 + (6.0)i_1 - (4.0)i_2 = 0$$6.0i_1 - 4.0i_2 = 24.0$  --- $(iii)$From $(i)$,$i_3 = i_1 + i_2$. Substituting this into $(ii)$:$6.0i_1 + 2.0(i_1 + i_2) = 10.0$$8.0i_1 + 2.0i_2 = 10.0$  --- $(iv)$Solving $(iii)$ and $(iv)$:$(6.0i_1 - 4.0i_2 = 24.0) 	imes 1 \implies 6.0i_1 - 4.0i_2 = 24.0$$(8.0i_1 + 2.0i_2 = 10.0) 	imes 2 \implies 16.0i_1 + 4.0i_2 = 20.0$Adding these equations:$22.0i_1 = 44.0 \implies i_1 = 2.0 \, A$.

Find the value of current $i_1$ for the circuit shown in the figure. (in $, A$)

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