JEE Main 2017 · 8 Apr · Shift 1 · Physics Q17

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PhysicsSingle correct+4 / -1Question 17 of 90

A 9 V battery with internal resistance of 0.5 Ω 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 9 V battery B with 0.5 Ω internal resistance (voltmeter V across it) feeds an infinite ladder: each section has 1 Ω in the top rail, 1 Ω in the bottom rail and a 4 Ω rung; ammeter A₁ is in the top rail next to the battery, A₂ and A₃ in the first two rungs.

Reading of

A_1

is 2 A

Reading of

A_1

is 18 A

Reading of V is 9 V

Reading of V is 7 V

Answer and worked solution

Official answer: A

The ladder's resistance $R$ satisfies $R=2+\dfrac{4R}{4+R}$ , i.e. $R^2-2R-8=0$ , so $R=4\ \Omega$ . With the internal resistance the total is 4.5 Ω, and
$I=\frac9{4.5}=2\text{ A}$
through $A_1$ . The voltmeter reads $9-2\times0.5=8$ V.

Topics:Series and parallel resistors EMF and internal resistance

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JEE Main 2017 · 8 Apr · Shift 1, Physics question 17