# A $9\; V$ battery with internal resistance of $0.5\; Ω$ is connected across an infinite network as shown in the figure. All ammeters $A_1, A_2, A_3$ and voltmeter $V$ are ideal.

Choose correct statement.

$\begin{array}{1 1}(1)\; Reading\; of\; A_1 \;is\; 2\; A \\ (2)\; Reading\; of\; A_1\; is\; 18\; A \\ (3)\; Reading\; of\; V\; is\; 9\; V \\ (4)\; Reading\; of\; V\; is\; 7\; V \end{array}$

\begin{align*} X = \frac{4X}{4 + X} + 2 \end{align*}
\begin{align*} X = \frac{8 + 6X}{4 + X} \end{align*}
$4X + X^2 = 8 + 6X$
$X^2 - 2X -8 = 0$
\begin{align*}X &= \frac{2 \pm \sqrt{4 -4(1)(-8) }}{2} \\ & = \frac{2 \pm \sqrt {36}}{2} \\ & = \frac{2 \pm 6}{2} = 4 \\A' &= \frac{9}{4 + 0.5} = 2 \\ A' & = 9\end{align*}