JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Current Electricity

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

(A) $1 : 4$
(B) $1 : 2$ ✓ Correct
(C) $4 : 1$
(D) $2 : 1$

Answer: (B)

Solution

Let the lengths be

ℓ_{X}

and

ℓ_{Y}

with

ℓ_{X} + ℓ_{Y} = 1

m.

For wires of same material and cross-section:

\frac{R _{X}}{R _{Y}} = \frac{ℓ _{X}}{ℓ _{Y}}

When wire X is stretched to double its length (to form W), the volume remains constant, so the cross-sectional area becomes half. Since

R \propto \frac{ℓ}{A}

, when length doubles and area halves, resistance becomes 4 times:

R_{W} = 4 R_{X}

Given:

R_{W} = 2 R_{Y}

Therefore:

4 R_{X} = 2 R_{Y}

→

\frac{R _{X}}{R _{Y}} = \frac{1}{2}

Thus:

\frac{ℓ _{X}}{ℓ _{Y}} = \frac{1}{2}

JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Single correct option

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JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Current Electricity

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