First slide

KVL

Question

Current through wire XY of circuit shown is

Moderate

A

1 A
B

4 A
C

2 A
D

3 A

Solution

$- i_{1} + 0 \times i_{xy} + 3 i_{2} = 0 or i_{1} = 3 i_{2}$ ….(i)
$Also, - 2 (i_{1} - i_{xy}) + 4 (i_{2} + i_{xy}) = 0$
$or 2 i_{1} - 4 i_{2} = 6 i_{xy}$ ….(ii)
$\begin{array}{l} Also, V_{AB} - 1 \times i_{1} - 2 (i_{1} - i_{xy}) = 0 \Rightarrow 50 = i_{1} + 2 (i_{1} - i_{xy}) \\ = 3 i_{1} - 2 i_{xy} \end{array}$ ….(iii)
Solving (i), (ii) and (iii), i_xy = 2A

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