Current Electricity - Result Question 7

8. A wire of resistance $4 \Omega$ is stretched to twice its original length. The resistance of stretched wire would be

[2013]

(a) $4 \Omega$

(b) $8 \Omega$

(c) $16 \Omega$

(d) $2 \Omega$

Show Answer

Answer:

Correct Answer: 8. (c)

Solution:

  1. (c) Resistance $R=\frac{\rho \ell}{A}=4 \Omega$

$\because \ell^{\prime}=2 \ell$

On stretching, volume of wire remains constant $\therefore \ell A^{\prime}=\ell^{\prime} A^{\prime}$

$\therefore A^{\prime}=\frac{A}{2}$

$\therefore R^{\prime} \rho \frac{2 \ell}{\frac{A}{2}}=4 R=4 \times 4 \Omega=16 \Omega \Rightarrow \ell A=2 \ell A^{\prime}$

Therefore the resistance of new wire becomes $16 \Omega$



NCERT Chapter Video Solution

Dual Pane