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

Answer 1

The correct option is A Reading of $A_1$ is 2 A.

$\frac{4x}{4+x}+2=x$

$4x+2(4+x)=n(4+x)$

$6x+8=4x+x^2$

$x^2-2x-8=0$

$x=2\pm \frac{\sqrt{4+32}}{2}$

$=\frac{216}{2}$

$=4\Omega$

$I=$ Current through $A_1=\frac{E}{r+R}=\frac{9}{0.5+4}=2A$

Potential $=V=E-1R=9-2\times 0.5$

$=8V$