The figure shows a circuit having eight resistances of $1 \Omega$ each, labelled $R_1$ to $R_8$, and two ideal batteries with voltages $\varepsilon_1=12 V$ and $\varepsilon_2=6 V$.
Which of the following statement($s$) is(are) correct?
$(A)$ The magnitude of current flowing through $R_1$ is $7.2 A$.
$(B)$ The magnitude of current flowing through $R_2$ is $1.2 A$.
$(C)$ The magnitude of current flowing through $R_3$ is $4.8 A$.
$(D)$ The magnitude of current flowing through $R_5$ is $2.4 A$.
IIT 2022, Advanced
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From $KCL$
$i _1+ i _2+ i _3=0$
$\Rightarrow \frac{18- V _0}{3 / 2}+\frac{12- V _0}{1 / 2}+\frac{0- V _0}{3 / 2}=0$
$\Rightarrow 18- V _0+36-3 V _0- V _0=0$
$\Rightarrow 54=5 V _0$
$\frac{2\left(\frac{54}{5}- v ^{\prime}\right)}{1}+\frac{18- v ^{\prime}}{1}=0 $
$\Rightarrow \frac{108}{5}+18=3 V ^{\prime}$
$\Rightarrow v ^{\prime}=\frac{198}{5 \times 3}=\frac{66}{5} V$
$I _{ R _1}=\frac{36}{5}=7.2 A$
$I _{ R _2}=\frac{6}{5}=1.2 A$
$I _{ R _3}=\frac{24}{5}=4.8 A$
$I _{ R _s}=\frac{12}{5}=2.4 A$
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