If the length of a copper wire is increased by 5% due to stretching. What will

Question

If the length of a copper wire is increased by $5 %$ due to stretching. What will be the percentage increase in its resistance?

Options:

A .

12 %

B .

11.5 %

C .

20.25 %

D .

10.25 %

Answer: Option D
:
D
Resistance,

R = ρ \frac{L}{A}

where:

ρ

: Resistivity,

L

: Length of the wire

A

: Cross-sectional area of the wire.
The length of the copper wire is increased by

5 %

.
So, new length is:

L^{'} = L + \frac{5}{100} L = 1.05 L

Let the new cross-sectional area be

A^{'}

.
On stretching the wire, its volume will remain constant.

⟹ L A = L^{'} A^{'}

A^{'} = \frac{A}{1.05}

New resistance will become:

R^{'} = ρ \frac{L^{'}}{A^{'}}

R^{'} = ρ (\frac{1.05 L}{A / 1.05})

R^{'} = {1.05}^{2} R = 1.1025 R

Percentage increase in its resistance is,

p = \frac{R^{'} - R}{R} \times 100

p = \frac{(1.1025 - 1) R}{R} \times 100

p = 10.25 %

Was this answer helpful ?

Next Question

Chapter 1 - GLOBAL STEEL SCENARIO & INDI Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Chapter 3.1 : Overview of Finance & Acco Chapter 3 : Finance & Accounts SAIL E0 - GFM 2024

Chapter 2.1 : Overview Chapter 2 : Materials Management SAIL E0 - GFM 2024

Chapter 1.1 : Personnel Functions- An ov Chapter 1 : Personnel Management SAIL E0 - GFM 2024

GPOE / GPA Combined 1 Free CBT Mock Test SAIL E0 2024

CBT Mixed Test 1 GPOE/GPA SAIL E0 2024