Question 119 of 380

In the following circuit, the magnitude of current ${I}_{1}$, is ______ $A$.

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Answer: 2

The figure above shows the current and voltage at different points in circuit.
Applying Kirchhoff's Junction law at $A$,
$\dfrac{x-(y+5)}{1}+\dfrac{x-2}{2}+\dfrac{x-0}{2}=0...\left(1\right)$
Applying Kirchhoff's Junction law at $B$,
$\dfrac{y+5-x}{1}+\dfrac{y-0}{1}+\dfrac{y-2}{1}=0...\left(2\right)$
Solving equation (1) and (2), we get
$x=3$ and $y=0$
Now, at $D$ junction
${I}_{1}={i}_{1}+{i}_{2}$
$\Rightarrow {I}_{1}=\dfrac{y-0}{1}+\dfrac{x-0}{2}$
$=\dfrac{0-0}{1}+\dfrac{3-0}{2}$
$\Rightarrow {I}_{1}=1.5A$.

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