The electric resistance of a certain wire of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The resistance of a wire is given by the formula $R = \rho \frac{L}{A}$,where $\rho$ is the resistivity (specific resistance),$L$ is the length,an

Vedclass · Accepted Answer

The resistance will be halved and the specific resistance will remain unchanged.

Vedclass · Answer

(B) The resistance of a wire is given by the formula $R = \rho \frac{L}{A}$,where $\rho$ is the resistivity (specific resistance),$L$ is the length,and $A$ is the cross-sectional area.Given that the cross-sectional area $A = \pi r^2$,the initial resistance is $R = \rho \frac{L}{\pi r^2}$.When the length is doubled $(L' = 2L)$ and the radius is doubled $(r' = 2r)$,the new resistance $R'$ becomes:$R' = \rho \frac{L'}{\pi (r')^2} = \rho \frac{2L}{\pi (2r)^2} = \rho \frac{2L}{4 \pi r^2} = \frac{1}{2} \left( \rho \frac{L}{\pi r^2} \right) = \frac{R}{2}$.Since resistivity $(\rho)$ is a material property and does not depend on the dimensions of the wire,it remains unchanged.Therefore,the resistance is halved and the specific resistance remains unchanged.

The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled,then

Similar Questions

Why does the resistance of metallic conductors and semiconductors change differently with a change in temperature?

The conductivity of a superconductor is

The conductivity of a conductor decreases with temperature because,on heating:

What is conductivity? On which factors does its value depend? Write its unit and dimension.

Vedclass Test Series

Exam Paper Generator

Online Exam Module