Two metallic wires of identical dimensions ar | vedclass

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

Question

(B) Let the length of each wire be $\ell$ and the cross-sectional area be $A$.For the equivalent wire,the total length is $2\ell$ and the cross-sectio

Vedclass · Accepted Answer

$\frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}$

Vedclass · Answer

(B) Let the length of each wire be $\ell$ and the cross-sectional area be $A$.For the equivalent wire,the total length is $2\ell$ and the cross-sectional area is $A$.The resistance of a wire is given by $R = \frac{\ell}{\sigma A}$,where $\sigma$ is the conductivity.Since the wires are connected in series,the equivalent resistance $R_{eq}$ is the sum of individual resistances:$R_{eq} = R_{1} + R_{2}$Substituting the formula for resistance:$\frac{2\ell}{\sigma_{eq} A} = \frac{\ell}{\sigma_{1} A} + \frac{\ell}{\sigma_{2} A}$Dividing both sides by $\frac{\ell}{A}$:$\frac{2}{\sigma_{eq}} = \frac{1}{\sigma_{1}} + \frac{1}{\sigma_{2}}$$\frac{2}{\sigma_{eq}} = \frac{\sigma_{1} + \sigma_{2}}{\sigma_{1} \sigma_{2}}$Therefore,the effective conductivity is $\sigma_{eq} = \frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1} + \sigma_{2}}$.

Two metallic wires of identical dimensions are connected in series. If $\sigma_{1}$ and $\sigma_{2}$ are the conductivities of these wires respectively,the effective conductivity of the combination is:

Similar Questions

$A$ rod of a certain metal is $1.0 \, m$ long and $0.6 \, cm$ in diameter. Its resistance is $3.0 \times 10^{-3} \, \Omega$. Another disc made of the same metal is $2.0 \, cm$ in diameter and $1.0 \, mm$ thick. What is the resistance between the round faces of the disc?

If a copper wire is stretched to make its radius decrease by $0.1\%$,then the percentage increase in resistance is approximately .......... $\%$

$A$ wire of radius $r$ has resistance $R$. If it is stretched to a radius of $\frac{3r}{4}$,its resistance becomes

The cross-sections of wires made of the same material and having the same length are shown in the figure. What can be said about their resistances?

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module