QJEEM17Ph0e34: JEE Main 2017 Physics - Class 12 JEEM17Ph0e34 Solution: A 9 V battery with internal resistance of 0.5 is connected…

Assume equivalent resistance of the infinite network is x.

The circuit can be redrawn like this,


Here 4 $\Omega$ and x $\Omega$ are parallel,

$\therefore\,\,\,$ ${1 \over {{x_{eq}}}}$ = ${1 \over 4}$ + ${1 \over x}$

$\Rightarrow$ $\,\,\,$ x_eq = ${{4x} \over {4 + x}}$

$\therefore\,\,\,$ Equivalent resistance between point A and B is ,

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

$\Rightarrow$ $\,\,\,$ x = ${{8 + 6x} \over {4 + x}}$

$\Rightarrow$ $\,\,\,$ 4x + x² = 8 + 6x

$\Rightarrow$ $\,\,\,$ x² $-$ 2x $-$ 8 = 0

$\Rightarrow$ $\,\,\,$ x = ${{2 \pm \sqrt {4 - 4\left( 1 \right)\left( { - 8} \right)} } \over 2}$

$\Rightarrow$ $\,\,\,$ x = ${{2 \pm 6} \over 2}$

$\Rightarrow$ $\,\,\,$ = 4 $\Omega$

(as negative value of x is not acceptable)

$\therefore\,\,\,$ Reading of Aonmeter, A₁ = ${V \over {R + r}}$

A₁ = ${9 \over {4\,\, + 0.5}}$ = 2 A