Question

A wire of resistance 3 ohm is stretched to double its length, such that its volume remains constant. The resistance of the stretched wire is
1 point
(a) 14 ohm
(b) 16 ohm
(c) 20 ohm
(d) 12 ohm

Answer 1

Answer:

d. 12 ohm

Explanation:

Let the resistance of wire when it is normal

$R = \rho \frac{l}{A}$

$3 \frac{A}{l} = \rho \dashleftarrow(1)$

Now when it is stretched, the lenght will be doubled and the area of cross section will be halved.

${R}^{i} = \rho \frac{2 l}{ \frac{A}{2}}$

${R}^{i} = 3 \frac{ \not A}{ \not \: l} \times \frac{2 \not \: l}{ \not A} \times 2 \dashleftarrow(from \: 1)$

${R}^{i} = 3 \times 2 \times 2$

$\boxed{{R}^{i} = 12 ohm}$

Hence the new resistance will be 12 ohm.