Find the percentage increase in resistance of a wire when it is stretched uniformly so that its length increases by 0.5 %

Question

Find the percentage increase in resistance of a wire when it is stretched uniformly so that its length increases by 0.5 %  (A)  1 %  (B)  2 %  (C)  2.5 %  (D)  3 %

Tardigrade Admin · Accepted Answer

As volume remains constant in the process of stretching

∴ V = A l

= constant

0 = \frac{Δ A}{A} + \frac{Δ l}{l}

or

∣ ∣ \frac{Δ A}{A} ∣ ∣ = ∣ ∣ \frac{Δ l}{l} ∣ ∣ \dots (i)

Resistance,

R = ρ \frac{l}{A}

∴ \frac{Δ R}{R} = ∣ ∣ \frac{Δ l}{l} ∣ ∣ + ∣ ∣ \frac{Δ A}{A} ∣ ∣

(∵ ρ

is constant)

\frac{Δ R}{R} = 2 ∣ ∣ \frac{Δ l}{l} ∣ ∣

(using eqn. (i))

∴ %

increase in resistance of wire

= 2 \times 0.5%

= 1%

Q. Find the percentage increase in resistance of a wire when it is stretched uniformly so that its length increases by $0.5%$

$1%$

$2%$

$2.5%$

$3%$

Q. Find the percentage increase in resistance of a wire when it is stretched uniformly so that its length increases by 0.5%

1%

2%

2.5%

3%

Q. Find the percentage increase in resistance of a wire when it is stretched uniformly so that its length increases by $0.5%$

$1%$

$2%$

$2.5%$

$3%$