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 $R$ of a wire is given by the formula $R = \rho \frac{l}{A} = \rho \frac{l}{\pi r^2}$,where $\rho$ is the resistivity (specific res

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) The resistance $R$ of a wire is given by the formula $R = ho \frac{l}{A} = ho \frac{l}{\pi r^2}$,where $ho$ is the resistivity (specific resistance),$l$ is the length,and $r$ is the radius.From this,we see that $R \propto \frac{l}{r^2}$.Let the initial length be $l_1 = l$ and initial radius be $r_1 = r$. The new length is $l_2 = 2l$ and the new radius is $r_2 = 2r$.The new resistance $R_2$ is given by:$\frac{R_2}{R_1} = \frac{l_2}{l_1} 	imes \left( \frac{r_1}{r_2} ight)^2 = \left( \frac{2l}{l} ight) 	imes \left( \frac{r}{2r} ight)^2 = 2 	imes \left( \frac{1}{2} ight)^2 = 2 	imes \frac{1}{4} = \frac{1}{2}$.Therefore,$R_2 = \frac{R}{2}$.Specific resistance (resistivity) $ho$ is a material property and does not depend on the dimensions (length or radius) of the wire. Thus,it remains unchanged.

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

Similar Questions

Which one of the following is used as an acid flux in metallurgy?

The magnifying power of a refracting type of astronomical telescope is $m$. If the focal length of the eyepiece is doubled,the magnifying power will become:

Vegetative propagation in Pistia occurs by:

An auditorium has a volume of $10^5 \ m^3$ and a total absorption area of $2 \times 10^4 \ m^2$. Its average absorption coefficient is $0.2$. The reverberation time of the auditorium in seconds is:

In the following combinations of logic gates,the outputs $A, B$ and $C$ are respectively

Vedclass Test Series

Exam Paper Generator

Online Exam Module