Question

If a wire of 1 Ω resistance is stretched to double its length then resistance will become ______.

पर्याय

• `1/2  Ω`

• 2 Ω

• `1/4  Ω`

• 4 Ω

Answer 1

If a wire of 1 Ω resistance is stretched to double its length then resistance will become 4 Ω.

Explanation:

Given: Initial resistance, \(R=1\,\Omega\)

Initial length, \(L\)

New length, \(L'=2L\)

When a wire is stretched, its volume remains constant. Therefore, its cross-sectional area becomes half.

Using the formula,

\[ R=\rho\frac{L}{A} \]

Since resistance is directly proportional to the square of the length,

\[ R'=R\left(\frac{L'}{L}\right)^2 \]

\[ =1\times\left(\frac{2L}{L}\right)^2 \]

\[ =1\times(2)^2 \]

\[=1\times4 \]

\[ {=4\,\Omega} \]