Question

Calculate the time constant ti of a straight solenoid of length l = 1.0 m having a single-layer winding of copper wire whose total mass is equal to m = 1.0 kg. The cross-sectional diameter of the solenoid is assumed to be considerably less than its length. 

Note. The time constant ti is the ratio L/R, where L is inductance and R is active resistance.

Answer 1

The time constant τ is given by

where, ρ₀ = resistivity, l₀ = length of the winding wire, S = cross section of the wire. 

But    m = lρ₀s

(note the interchange of l and l₀ because of difference in notation here.)