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### JEE Main 2017 (Online) 8th April Morning Slot

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, 3 and voltmeter V are ideal.
Choose correct statement.
A
Reading of A1 is 2 A
B
Reading of A1 is 18 A
C
Reading of   V   is  9 V
D
Reading of   V   is   7 V

## Explanation

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 $$\,\,\, xeq = {{4x} \over {4 + x}} \therefore\,\,\, Equivalent resistance between point A and B is , x = {{4x} \over {4 + x}} + 2 \Rightarrow$$\,\,\,$ 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
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### JEE Main 2017 (Online) 9th April Morning Slot

A uniform wire of length 1 and radius r has a resistance of 100 $\Omega$. It is recast into a wire of radius ${r \over 2}.$ The resistance of new wire will be :
A
1600 $\Omega$
B
400 $\Omega$
C
200 $\Omega$
D
100 $\Omega$

## Explanation

Resistance of a wire of length l and radius r is given by

R = ${{\rho l} \over A}$ = ${{\rho l} \over A} \times {A \over A} = {{\rho V} \over {{A^2}}} = {{\rho V} \over {{\pi ^2}{r^4}}}$

$\Rightarrow$ R $\propto$ ${1 \over {{r^4}}}$

$\therefore$ ${{{R_1}} \over {{R_2}}} = {\left( {{{{r_2}} \over {{r_1}}}} \right)^4}$

Given, R1 = 100 $\Omega$, r1 = r, r2 = ${r \over 2}$ , R2 = ?

$\therefore$ R2 = R1${\left( {{{{r_1}} \over {{r_2}}}} \right)^4}$ = 16R1 = 1600 $\Omega$
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### JEE Main 2017 (Online) 9th April Morning Slot

In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance P = 4 $\Omega$ and the neutral point N is at 60 cm from A. Now an unknown resistance R is connected in series to P and the new position of the neutral point is at 80 cm from A. The value of unknown resistance R is :

A
${{33} \over 5}\,\Omega$
B
6 $\,\Omega$
C
7 $\,\Omega$
D
${{20} \over 3}\,\Omega$
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### JEE Main 2017 (Online) 9th April Morning Slot

The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P1 , P2 and P3 respectively, then :

A
P1 > P2 > P3
B
P1 > P3 > P2
C
P2 > P1 > P3
D
P3 > P2 > P1