Two metal wires of the same length and same a | 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 $R = \frac{L}{\sigma A}$,where $L$ is the length,$A$ is the cross-sectional area,and $\sigma$ is the conducti

Vedclass · Accepted Answer

$\frac{2 \sigma_1 \sigma_2}{\sigma_1+\sigma_2}$

Vedclass · Answer

(B) The resistance of a wire is given by $R = \frac{L}{\sigma A}$,where $L$ is the length,$A$ is the cross-sectional area,and $\sigma$ is the conductivity.For two wires connected in series,the total resistance is $R_{eq} = R_1 + R_2$.The total length of the combined wire is $2L$,and the area remains $A$.Substituting the expressions for resistance: $\frac{2L}{\sigma_{eq} A} = \frac{L}{\sigma_1 A} + \frac{L}{\sigma_2 A}$.Canceling $L$ and $A$ from both sides,we get: $\frac{2}{\sigma_{eq}} = \frac{1}{\sigma_1} + \frac{1}{\sigma_2}$.Simplifying the right side: $\frac{2}{\sigma_{eq}} = \frac{\sigma_1 + \sigma_2}{\sigma_1 \sigma_2}$.Therefore,the effective conductivity is $\sigma_{eq} = \frac{2 \sigma_1 \sigma_2}{\sigma_1 + \sigma_2}$.

Two metal wires of the same length and same area of cross-section have conductivities of their material $\sigma_1$ and $\sigma_2$. If they are connected in series,the effective conductivity is:

Similar Questions

$n$ conducting wires of same dimensions but having resistivities $1, 2, 3, . . . , n$ are connected in series. The equivalent resistivity of the combination is

The dimensions of resistivity in terms of $M, L, T$ and $Q$,where $Q$ stands for the dimensions of charge,is:

$A$ metal rod of length $10 \text{ cm}$ and a rectangular cross-section of $1 \text{ cm} \times 0.5 \text{ cm}$ is connected to a battery across opposite faces. The resistance will be . . . . . . .

The resistance of a wire of uniform diameter $d$ and length $L$ is $R$. The resistance of another wire of the same material but diameter $2d$ and length $4L$ will be

$A$ nichrome wire $50 \text{ cm}$ long and $1 \text{ mm}^2$ cross-section carries a current of $4 \text{ A}$ when connected to a $2 \text{ V}$ battery. The resistivity of the nichrome wire in $\Omega \cdot \text{m}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module