A 9 V battery with internal resistance of \[0.5\Omega \] is connected across an infinite network as shown in the figure. All ammeters A1, A2, A3 and voltmeter V are ideal. Choose correct statement. [JEE Online 08-04-2017]
A) Reading of \[{{A}_{1}}\] is 18 A
B) Reading of V is 9 V
C) Reading of V is 7 V
D) Reading of \[{{A}_{1}}\] is 2 A
Correct Answer: D
Solution :
\[x=\frac{4x}{4+x}+2\] \[x=\frac{8+6x}{4+x}\] \[4x+{{x}^{2}}=8+6x\] \[{{x}^{2}}-2x-8=0\] \[x=\frac{2\pm \sqrt{4-4(1)(-8)}}{2}=\frac{2\pm \sqrt{36}}{2}\] \[=\frac{2\pm 6}{2}=4\] \[A'=\frac{9}{4+0.5}=2\] A?= 9
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