$A$ wire of length $L$ and resistance $R$ is stretched so that the length is doubled and area of cross-section is halved. How will its
$(a)$ resistance change?
$(b)$ resistivity change?
$(a)$ resistance change?
$(b)$ resistivity change?
(A) $R = \rho \frac{L}{A}$
Where $R$ is the resistance and $\rho$ is the resistivity of the material.
Initial length of the wire $= L$. The new length is $L' = 2L$ and the new area of cross-section is $A' = A/2$.
$(a)$ The new resistance $R'$ is given by:
$R' = \rho \frac{L'}{A'} = \rho \frac{2L}{A/2} = 4 \left( \rho \frac{L}{A} \right) = 4R$.
Thus,the resistance becomes $4$ times the original resistance.
$(b)$ Resistivity $(\rho)$ is an intrinsic property of the material and depends only on the nature of the material and temperature. Therefore,it remains unchanged.
Where $R$ is the resistance and $\rho$ is the resistivity of the material.
Initial length of the wire $= L$. The new length is $L' = 2L$ and the new area of cross-section is $A' = A/2$.
$(a)$ The new resistance $R'$ is given by:
$R' = \rho \frac{L'}{A'} = \rho \frac{2L}{A/2} = 4 \left( \rho \frac{L}{A} \right) = 4R$.
Thus,the resistance becomes $4$ times the original resistance.
$(b)$ Resistivity $(\rho)$ is an intrinsic property of the material and depends only on the nature of the material and temperature. Therefore,it remains unchanged.
Explore More
Similar Questions
The unit of electric current,$.......$,is also called an ampere,named after André-Marie Ampère.
Easy
View Solution$A$ current of $1 \ A$ flows in a series circuit containing an electric lamp and a conductor of $5 \ \Omega$ when connected to a $10 \ V$ battery. Calculate the resistance of the electric lamp. Now,if a resistance of $10 \ \Omega$ is connected in parallel with this series combination,what change (if any) in the current flowing through the $5 \ \Omega$ conductor and the potential difference across the lamp will take place? Give reason.
Medium
View Solution$A$ wire is $1.0 \, m$ long,$0.2 \, mm$ in diameter and has a resistance of $10 \, \Omega$. Calculate the resistivity of its material.
Easy
View Solution$(a)$ Explain how a cell maintains current in a circuit.
$(b)$ In the circuit given below,the resistance of the path $xTy = 2 \, \Omega$ and that of $xZy = 6 \, \Omega$.
$(i)$ Find the equivalent resistance between $x$ and $y$.
$(ii)$ Find the current in the main circuit.
$(iii)$ Calculate the current that flows through the path $xTy$ and $xZy$.
$(b)$ In the circuit given below,the resistance of the path $xTy = 2 \, \Omega$ and that of $xZy = 6 \, \Omega$.
$(i)$ Find the equivalent resistance between $x$ and $y$.
$(ii)$ Find the current in the main circuit.
$(iii)$ Calculate the current that flows through the path $xTy$ and $xZy$.
Difficult
View Solution$(a)$ Derive an expression to find the equivalent resistance of three resistors connected in series. Also,draw the schematic diagram of the circuit.
$(b)$ Find the equivalent resistance of the following circuit.
$(b)$ Find the equivalent resistance of the following circuit.
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo