1
MCQ (Single Correct Answer)

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 $$\Omega $$
2
MCQ (Single Correct Answer)

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
3
MCQ (Single Correct Answer)

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
$${{20} \over 3}\,\Omega $$
4
MCQ (Single Correct Answer)

JEE Main 2018 (Offline)

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k$$\Omega $$. How much was the resistance on the left slot before interchanging the resistances?
A
910 $$\Omega $$
B
990 $$\Omega $$
C
505 $$\Omega $$
D
550 $$\Omega $$

Explanation



$${X \over l}$$ = $${{1000 - X} \over {100 - l}}$$ . . . . . (1)

When X and Y are interchanged.



$${{1000 - X} \over {l - 10}}$$ = $${X \over {100 - l + 10}}$$

$$ \Rightarrow $$$$\,\,\,$$ $${{1000 - X} \over {l - 10}}$$ = $${X \over {110 - l}}$$ . . . . . (2)

From (1) and (2) we get,

$${l \over {100 - l}}$$ = $${{110 - l} \over {l - 10}}$$

$$ \Rightarrow $$$$\,\,\,$$ $$l$$2 $$-$$ 10 = 11000 $$-$$ 100$$l$$ $$-$$ 110$$l$$ + $$l$$2

$$ \Rightarrow $$$$\,\,\,$$ 200$$l$$ = 11000

$$l$$ = 55 cm

Putting this value of $$l$$, in equation (1)

$${X \over {55}}$$ = $${{1000 - X} \over {100 - 55}}$$

$$ \Rightarrow $$$$\,\,\,$$ 45X = 55000 $$-$$ 55X

$$ \Rightarrow $$$$\,\,\,$$ 100X = 55000

$$ \Rightarrow $$$$\,\,\,$$ X = 550 $$\Omega $$

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