A cylindrical metal wire of length l and cross-sectional area S, has resistance R, conductance G, conductivity σ and resistivity ρ . Which one of the following expression for σ is valid?

Question

A cylindrical metal wire of length l and cross-sectional area S, has resistance R, conductance G, conductivity σ and resistivity ρ . Which one of the following expression for σ is valid? (A)  (GS/l)  (B)  (Rl/S)  (C)  (GR/ρ )  (D)  (ρ R/G)

Tardigrade Admin · Accepted Answer

We know that, conductivity σ =(1/ρ ) ?(i) and conductance, G=(1/R) ...(ii) ⇒ GR=1 From Eqs. (i) and (ii), we get σ =(GR/ρ )

Q. A cylindrical metal wire of length $l$ and cross-sectional area S, has resistance R, conductance G, conductivity $σ$ and resistivity $ρ$ . Which one of the following expression for $σ$ is valid?

$\frac{GS}{l}$

$\frac{Rl}{S}$

$\frac{GR}{ρ}$

$\frac{ρR}{G}$

We know that, conductivity $σ = \frac{1}{ρ}$ ?(i) and conductance, $G = \frac{1}{R}$ ...(ii) $\Rightarrow$ $GR = 1$ From Eqs. (i) and (ii), we get $σ = \frac{GR}{ρ}$

Q. A cylindrical metal wire of length l and cross-sectional area S, has resistance R, conductance G, conductivity σ and resistivity ρ . Which one of the following expression for σ is valid?

lGS​

SRl​

ρGR​

GρR​