In the circuit shown below $E_1\, =4.0\, V$, $R_1\, = 2\,\Omega$, $E_2\, = 6.0\, V$, $R_2\, = 4\,\Omega$ and $R_3\, = 2\,\Omega$. The current $I_1$ is ............... $\mathrm{A}$
Diffcult
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Applying Kirchhoff's law for the loops $(1)$ and $(2)$ as shown in figure
For loop $(1)$
$-2 i_{1}-2\left(i_{1}-i_{2}\right)+4=0$
$\Rightarrow 2 \mathrm{i}_{1}-\mathrm{i}_{2}=2$ .........$(i)$
For loop $(2)$
$-2\left(i_{1}-i_{2}\right)+4 i_{2}-6=0$
$\Rightarrow-\mathrm{i}_{1}+3 \mathrm{i}_{2}=3$ .........$(ii)$
On solving equation $(i)$ and $(ii),$ $\mathrm{i}_{1}=1.8 \mathrm{\,A}.$
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