What is the current in A flowing through BD i | vedclass

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(A) Let $i_1$ be the current in the left loop and $i_2$ be the current flowing through the resistor in branch $BD$.Applying Kirchhoff's Voltage Law $(

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$5$

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(A) Let $i_1$ be the current in the left loop and $i_2$ be the current flowing through the resistor in branch $BD$.Applying Kirchhoff's Voltage Law $(KVL)$ to the left loop (starting from $D$ to $A$ to $B$ to $D$):$15 - 6i_1 - 3i_2 = 0 \implies 6i_1 + 3i_2 = 15 \implies 2i_1 + i_2 = 5$ ... $(i)$Applying $KVL$ to the right loop (starting from $D$ to $B$ to $C$ to $D$):$-3(i_1 - i_2) - 30 + 3i_2 = 0$ (Note: The current through $BC$ is $i_1 - i_2$ based on the junction rule at $B$)$-3i_1 + 3i_2 + 3i_2 = 30 \implies -3i_1 + 6i_2 = 30 \implies -i_1 + 2i_2 = 10$ ... $(ii)$Multiplying equation $(i)$ by $1$ and equation $(ii)$ by $2$:$2i_1 + i_2 = 5$$-2i_1 + 4i_2 = 20$Adding the two equations:$5i_2 = 25 \implies i_2 = 5 \, A$.Thus,the current flowing through $BD$ is $5 \, A$.

What is the current in $A$ flowing through $BD$ in the given circuit?

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