Two metal wires of identical dimensions are c | 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 $R = \frac{\ell}{\sigma A}$,where $\ell$ is the length,$\sigma$ is the conductivity,and $A$ is the cross-sect

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) The resistance of a wire is given by $R = \frac{\ell}{\sigma A}$,where $\ell$ is the length,$\sigma$ is the conductivity,and $A$ is the cross-sectional area.For two wires connected in series,the equivalent resistance is $R_{eq} = R_1 + R_2$.Since the wires have identical dimensions,let the length of each wire be $\ell$ and the cross-sectional area be $A$.The equivalent resistance of the combination is $R_{eq} = \frac{2\ell}{\sigma_{eq} A}$.Substituting the expressions for $R_1$,$R_2$,and $R_{eq}$ into the series formula:$\frac{2\ell}{\sigma_{eq} A} = \frac{\ell}{\sigma_1 A} + \frac{\ell}{\sigma_2 A}$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 metal wires of identical dimensions are connected in series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the metal wires respectively,the effective conductivity of the combination is

Similar Questions

The equivalent resistance of the circuit shown below between points $a$ and $b$ is $..........\Omega$

$6 \Omega$ and $12 \Omega$ resistors are connected in parallel. This combination is connected in series with a $10 \text{ V}$ battery and a $6 \Omega$ resistor. What is the potential difference between the terminals of the $12 \Omega$ resistor (in $\text{ V}$)?

Four resistors,$100 \Omega, 200 \Omega, 300 \Omega$ and $400 \Omega$ are connected to form four sides of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diagonal of the square (in $Omega$)?

$3$ identical bulbs are connected in series and these together dissipate a power $P$. If now the bulbs are connected in parallel,then the power dissipated will be

$A$ wire of resistance $R$ is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of the equivalent resistance between the two end points of an edge of the triangle to that of the square is

Vedclass Test Series

Exam Paper Generator

Online Exam Module