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JEE Main 2022 (29 Jul, Shift 2) · Ohm's Law, Resistivity & Temperature

Ohm's Law, Resistivity & Temperature question from JEE Main 2022 (29 Jul, Shift 2)

Q31JEE Main 2022 · 29 JUL · SHIFT 2Difficult

Ohm's Law, Resistivity & Temperature

A $1\text{ m}$ long wire is broken into two unequal parts $\text{X}$ and $\text{Y}$ . The $\text{X}$ part of the wire is streched into another wire W. Length of $W$ is twice the length of $X$ and the resistance of $\text{W}$ is twice that of $\text{Y}$ . Find the ratio of length of $\text{X}$ and $\text{Y}$ .

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Answer: (b)

Let lengths be $x$ (X) and $y$ (Y); same wire, so $R = kl$ before stretching: $R_X = kx$ , $R_Y = ky$ .
Stretching X to twice its length (volume constant) multiplies resistance by $2^2$ : $R_W = 4kx$ .
$R_W = 2R_Y \Rightarrow 4kx = 2ky \Rightarrow x : y = 1 : 2$
The answer is (b).

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