Q 12-03-288JEE MainJEE Main 2017 (8 Apr)Medium
A $9$ V battery with an internal resistance of $0.5\ \Omega$ 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 the correct statement.
Answer: (D) Reading of $A_1$ is $2$ A.
Let the resistance of the infinite network be $R$. Removing the first section leaves the same infinite network, so
$$R = 1 + 1 + \frac{4R}{4 + R}$$
$$R(4 + R) = 2(4 + R) + 4R \;\Rightarrow\; R^2 - 2R - 8 = 0 \;\Rightarrow\; R = 4\ \Omega$$
Current from the battery (read by $A_1$):
$$I = \frac{9}{4 + 0.5} = 2\ \text{A}$$
The voltmeter reads the terminal voltage $9 - 2(0.5) = 8$ V, so only statement (4) is correct.
Solution by Sreeraj P, M.Sc Physics