The current from the battery in the given cir | vedclass

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Question

(A) According to the circuit diagram,let $i_1$ be the current flowing through the left loop and $i_2$ be the current flowing through the right loop.Ap

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) According to the circuit diagram,let $i_1$ be the current flowing through the left loop and $i_2$ be the current flowing through the right loop.Applying Kirchhoff's voltage law $(KVL)$ in the left loop (mesh $I$):$2i_1 + 6(i_1 - i_2) + 8i_1 + 0.5i_1 - 15 = 0$$16.5i_1 - 6i_2 = 15 \dots (I)$Applying Kirchhoff's voltage law $(KVL)$ in the right loop (mesh $II$):$7i_2 + 1i_2 + 10i_2 + 6(i_2 - i_1) = 0$$24i_2 - 6i_1 = 0$$4i_2 = i_1 \dots (II)$Substituting equation $(II)$ into equation $(I)$:$16.5(4i_2) - 6i_2 = 15$$66i_2 - 6i_2 = 15$$60i_2 = 15$$i_2 = 0.25 \, A$Now,find $i_1$ using equation $(II)$:$i_1 = 4 	imes 0.25 = 1 \, A$The current from the battery is $i_1 = 1 \, A$.

The current from the battery in the given circuit is ................ $A$.

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