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

Answer

A

Explanation

For a solenoid, `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 = axD`
`Rm = (rhox)/(a) axD, x = sqrt((Rm)/(rho D))`
Also, `x = 2 pi rN, N = (x)/(2 pir) ( :. L = (mu_(0)N^(2)A)/(l))`
`:. L = mu_(0)((x)/(2pir))^(2) (pir^(2))/(l) = (mu_(0))/(4 pil) (Rm)/(rhoD)`