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))/(4 pi l)(Rm)/(rho D)`
B. `(mu_(0))/(4 pi l)(lm)/(rho D)`
C. `(mu_(0))/(4 pi l)(R^(2)m)/(rho D)`
D. `(mu_(0))/(2 pi R)(l m)/(rho D)`

Answer

A

Explanation

For a sloenoid, `L = mu_(0) N^(2)(A)/(l)`. If `x` is the length of the wire and `a` is the area of cross-section, then
`R = (rho x)/(a)` and `m = a xD`
`Rm = (rho x)/(a) a x D, x = ((R m)/(rho D))`
Also, `x = 2 pi rN, N = (X)/(2pi r) ( :. L = (mu_(0)N^(2)A)/(l))`
`:. L = mu_(0)((x)/(2pir))^(2) (pi r^(2))/(l) = (mu_(0))/(4pi l)(Rm)/(rho D
)`