Resistivity of potentiometer wire is `10^(-7)Omega-m` and its area of cross-section is `10^(-6)Omegam^(2)`. When a current i=0.1A flows through the wire, its potential gradient is

Options

A. `10^(-2) V//m`
B. `10^(-4)V//m`
C. 0.1 V/m
D. 10 V/m

Answer

A

Explanation

Potential gradient of a wire equal to potential fall per unit length.
Potential gradient =Potential fall per unit length
= Current x Resistance per unit length `=i=R/l`
But `R=(rhol)/A rArr R/l=(rho)/A`
`:.` Potential gradient `=ixx(rho)/A`
Here, `rho=10^(-7) Omega-m, i=0.1 AxxA =10^(-6) m^(2)`
Hence, potential gradient `=0.1xx(10^(-7))/(10^(-6)) =0.1/10=0.01 =10^(-2) V//m`