A wire of resistance 2? is stretched to double its length. What is the new resisters of the wire .

When a wire is stretched to double its length, its resistance changes due to the physical properties of the material. To understand how this works, let's break it down step by step.

Understanding Resistance in Wires

The resistance \( R \) of a wire is given by the formula:

R = ρ (L/A)

Where:

• R = resistance
• ρ = resistivity of the material (a constant for a given material)
• L = length of the wire
• A = cross-sectional area of the wire

Effects of Stretching the Wire

When the wire is stretched to double its length, several changes occur:

• The new length \( L' \) becomes \( 2L \).
• The volume of the wire remains constant during stretching. Therefore, if the length doubles, the cross-sectional area must decrease to maintain the same volume.

Calculating the New Cross-Sectional Area

The volume \( V \) of the wire can be expressed as:

V = L × A

When the wire is stretched, the volume remains constant:

L × A = L' × A'

Substituting \( L' = 2L \), we get:

L × A = 2L × A'

From this, we can simplify to find the new area:

A' = A / 2

Finding the New Resistance

Now, we can substitute the new values into the resistance formula:

R' = ρ (L' / A')

Substituting \( L' = 2L \) and \( A' = A / 2 \):

R' = ρ (2L / (A / 2))

This simplifies to:

R' = ρ (2L) × (2 / A) = 4 × (ρ (L / A))

Since \( R = ρ (L / A) \), we can substitute:

R' = 4R

Final Result

Given that the original resistance \( R \) of the wire is 2 ohms, the new resistance after stretching the wire to double its length will be:

R' = 4 × 2 = 8 ohms

In summary, when the wire is stretched to double its length, its resistance increases to 8 ohms due to the changes in both length and cross-sectional area. This illustrates how physical alterations to a conductor can significantly impact its electrical properties.