Current Electricity - Result Question 19

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20. If a wire of resistance $R$ is melted and recasted to half of its length, then the new resistance of the wire will be

======= ####20. If a wire of resistance $R$ is melted and recasted to half of its length, then the new resistance of the wire will be

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/current-electricity/current-electricity—result-question-19.md (a) $R / 4$

(b) $R / 2$

(c) $R$

(d) $2 R$

[1995]

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Answer:

Correct Answer: 20. (a)

Solution:

  1. (a) Initial resistance $(R_1)=R$; Initial length is $\ell_1$ and final length $(\ell_2)=0.5 \ell$. Volume of a wire $=\ell . A$. Since the volume of the wire remains the same after recasting, therefore $\ell_1 \cdot A_1=\ell_2$ $A_2$

or $\frac{\ell_1}{\ell_2}=\frac{A_2}{A_1}$ or $\frac{\ell}{0.5 \ell}=\frac{A_2}{A_1}$ or $\frac{A_2}{A_1}=2$.

We also know that resistance of a wire $(R)$

$R=\rho \times \frac{\ell}{A} . ; R \propto \frac{\ell}{A}$

$\therefore \frac{R_1}{R_2}=\frac{\ell_1}{\ell_2} \times \frac{A_2}{A_1}=\frac{\ell}{0.5 \ell} \times 2=4$

or , $R_2=\frac{R_1}{4}=\frac{R}{4}$.

When wires are drawn from same volume but with different area of cross-section, then

$R \propto \frac{1}{(\text{ Area of cross-section })^{2}}$