A wire of $1 \Omega$ has a length of $1 \mathrm{~m}$. It is stetched till its length increases by $25 \%$. The percentage change in resistance to the neartest integer is :-
$56 \%$
$25 \%$
$12.5 \%$
$76 \%$
Correct Option: 1
As volume of wire remains constant so
$\mathrm{A}_{0} \ell_{0}=\mathrm{A}_{1} \ell_{1} \Rightarrow \mathrm{A}_{1}=\frac{\ell_{0} \mathrm{~A}_{0}}{\ell_{1}}$
Now
$\operatorname{Resistance}(\mathrm{R})=\frac{\rho \ell}{\mathrm{A}}$
$\frac{\mathrm{R}_{0}}{\mathrm{R}_{1}}=\frac{\ell_{0} / \mathrm{A}_{0}}{\rho \ell_{1} / \mathrm{A}_{1}}$
$\frac{1}{\mathrm{R}_{1}}=\frac{\ell_{0}}{\mathrm{~A}_{0}}\left(\frac{\ell_{0} \mathrm{~A}_{0}}{\ell_{1} \times \ell_{1}}\right) \quad \mathrm{R}_{1}=\frac{\ell_{1}^{2}}{\ell_{0}^{2}}=1.5625 \Omega$
So $\%$ change in resistance
$=\frac{\mathrm{R}_{1}-\mathrm{R}_{0}}{\mathrm{R}_{0}} \times 100 \%$
$=\frac{1.5625-1}{1} \times 100 \%$
$=56.25 \%$
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,