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

$A$ negligibly small current is passed through a wire of length $15 \; m$ and uniform cross-section $6.0 \times 10^{-7} \; m^{2},$ and its resistance is measured to be $5.0 \; \Omega .$ What is the resistivity of the material at the temperature of the experiment?

The resistance of a wire at $300 \, K$ is found to be $0.3 \, \Omega$. If the temperature coefficient of resistance of the wire is $1.5 \times 10^{-3} \, K^{-1}$, the temperature at which the resistance becomes $0.6 \, \Omega$ is: (in $K$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module