Question

A $9 \,V$ battery with 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 correct statement.

• A. Reading of $A_1$ is 2 A
• B. Reading of $A_1$ is 18 A
• C. Reading of V is 9 V
• D. Reading of V is 7 V

Answer 1

Answer: (A)

$x = \frac{4x}{4+x}+2$
$x = \frac{8+6x}{4+x}$
$4x + x^{2} = 8 + 6x$
$x^{2} - 2x - 8 = 0$
$x = \frac{2\pm\sqrt{4-4\left(1\right)\left(-8\right)}}{2} = \frac{2\pm\sqrt{36}}{2}$
$= \frac{2\pm6}{2} = 4$
$A' = \frac{9}{4+0.5} = 2$
$A' = 9$