Question

Q19. I need an answer quick please.

Answer 1

Solution given in attachment mate .......

Answer 2

Question-19)

▪ A piece of wire of resistance 4Ω is stretched such that its area of cross-section becomes one-fourth of its original, then the resistance is

A) 8 ohms

B) 64 ohms

C) 2 ohms

D) 16 ohms

Concept :

✏ This question is completely based on concept of volume conservation.

Calculation :

$\implies\bf\:V_{initial}=V_{final}\\ \\ \implies\sf\:A_1L_1=A_2L_2\\ \\ \implies\sf\:A\times L_1=\dfrac{A}{4}\times L_2\\ \\ \implies\bf\pink{L_2=4L_1}\\ \\ \star\:\:\bf\orange{R=\rho\times \dfrac{L}{A}}\\ \\ \implies\sf\:\dfrac{R_1}{R_2}=\dfrac{L_1\times A_2}{A_1\times L_2}\\ \\ \implies\sf\:\dfrac{4}{R_2}=\dfrac{L\times \frac{A}{4}}{4L\times A}\\ \\ \implies\sf\:\dfrac{4}{R_2}=\dfrac{1}{16}\\ \\ \implies\boxed{\bf{\purple{R_2=64\:\Omega}}}$

▶Option B is correct