The inductance `L` of a solenoid of length `l`, whose windings are made of material of density `D` and resistivity `rho`, is (the winding resistance is`R`)

Options

A. `(mu_0)/(4pil)(Rm)/(rhoD)`
B. `(mu_0)/(4pir)(lm)/(rhoD)`
C. `(mu_0)/(4pil)(R^2m)/(rhoD)`
D. `(mu_0)/(2piR)(lm)/(rhoD)`

Answer

A

Explanation

For a solenoid `L=mu_0N^2A/l` . If x is the length of the wire and a is the area of cross-section, then `R=(rhox)/a and m=axD`
`Rm=(rhox)/a axD,x=sqrt((Rm)/(rhoD))`
Also, `x=2pirN,N=x/(2pir)therefore L=(mu_0N^(2)A/(l)`
`therefore L=mu_0(x./(2pir))^2(pir^2)/l=(mu_0)/(4pil)(Rm)/(rhoD)`