Question

A thick wire of resistance 25 ohm is drawn into a
wire such that its length becomes four times.
new resistance of the wire will be
(a) 50 ohm
(c) 100 ohm
(b) 25 ohm
(d) 400 ohm
​

Answer 1

Answer:

the answer is 100 ohms

Explanation:

because length is directly proportional to resistance

Answer 2

Answer:

The new resistance of the wire is 400 ohms.

Explanation:

• The resistance of a wire of cross section area, A and length, L is given by

$R = \frac{ρL}{A}$

• where, ρ is resistivity of the material.

Given that :

• Resistance of thick wire is 25 ohms.
• Length is stretched to 4 times its original length

To find :

• New resistance of wire

Solution :

• The original length of the wire is

$25 = \frac{ρL}{A} \: \: - - - (1)$

• If the length of the wire is stretched to 4 times its length, there must be some reduction in cross sectional area, A.
• Let, the length of new wire be L' and cross sectional area be A' .
• Since, the volume of the wire is constant through the process.

$LA = L'A' \\ A' = \frac{LA}{L'} \\ A' = \frac{AL}{4L} \\ A' = \frac{A}{4}$

• Let, the new resistance of the wire be R'.

$R' = \frac{ρL'}{A'} = \frac{ρ4L}{ (\frac{A}{4} )} \\ = \frac{ρ16L}{A} \\ = 25 \times 16 \\ R'= 400 \: ohms$

• Hence, resistance of new length is 400 ohms.