Question

The resistance of a wire is R the wire is stretched to doubled its length resistance of the wire becomes:

• A. R/2
• B. 4R
• C. 2R
• D. R/4

Answer 1

Answer:

B. 4R

• The electrical resistance (R) of a wire is determined by its material resistivity (ρ), length (L), and cross-sectional area (A).

• The formula for resistance is R = ρ * (L / A).

• Resistivity (ρ) is an intrinsic property of the material itself.

Effect of Stretching a Wire

• When a wire is stretched, its volume remains constant (assuming no material is lost).

• If the length of the wire is increased, its cross-sectional area must decrease proportionally to maintain constant volume.

• Let the original length be L₁ and the original cross-sectional area be A₁. The original resistance R₁ = ρ * (L₁ / A₁).

• If the wire is stretched to double its length, the new length L₂ = 2 * L₁.

• Since the volume (V = L * A) is constant, V₁ = V₂, which means L₁ * A₁ = L₂ * A₂.

• Substituting L₂ = 2 * L₁, we get L₁ * A₁ = (2 * L₁) * A₂.

• This implies that the new cross-sectional area A₂ = A₁ / 2.

• The new resistance R₂ = ρ * (L₂ / A₂).

• Substituting the new length and area: R₂ = ρ * ((2 * L₁) / (A₁ / 2)).

• Simplifying this expression: R₂ = ρ * (4 * L₁ / A₁).

• Since the original resistance R₁ = ρ * (L₁ / A₁), we can substitute R₁ into the equation for R₂.

• Therefore, R₂ = 4 * (ρ * L₁ / A₁) = 4 *R₁.

• If the original resistance of the wire is R, and its length is doubled by stretching, the new resistance becomes 4R.