A cylindrical metal wire of length $l$ and cross sections area $S$, has resistance $R$, conductance $G$, conductivity $\sigma$ and resistivity $\rho$. Which one of the following expressions for $\sigma$ is valid
A$\frac{{GR}}{\rho }$
B$\frac{{\rho R}}{G}$
C$\frac{{GS}}{l}$
D$\frac{{Rl}}{S}$
Medium
Download our app for free and get started
A$\frac{{GR}}{\rho }$
a Conductivity $\sigma = \frac{1}{\rho }$ .... $(i)$
and conductance $G = \frac{1}{R}$
$ \Rightarrow \,\,GR = 1$ ..... $(ii)$
From equation $(i)$ and $(ii)$ $\sigma = \frac{{GR}}{\rho }$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Consider a thin square sheet of side $\mathrm{L}$ and thickness $\mathrm{t}$, made of a material of resistivity $\rho$. The resistance between two opposite faces, shown by the shaded areas in the figure is
In the electric network shown, when no current flows through the $4 \Omega$ resistor in the arm EB, the potential difference between the points $A$ and $D$ will be $.............\,V$
Four resistances $40 \ \Omega, 60\ \Omega, 90\ \Omega$ and $110\ \Omega$ make the arms of a quadrilateral $A,B,C,D$. Across $AC$ is a battery of emf $40\, V$ and internal resistance negligible. The potential difference across $BD$ is $V$ is......
In the circuit shown, a four wire potentiometer is made of a $400\, cm$ long wire, which extends between $A$ and $B$. The resistance per unit length of the potentiometer wire is $r = 0.01\, \Omega /cm$. If an ideal voltmeter is connected as shown with jockey $J$ at $50\, cm$ from end $A$, the expected reading of the voltmeter will be: ............... $V$