An AWG 24 copper wire with a diameter of 0.511 mm is tightly wrapped (one turn per wire diameter) around a2.54-cm-diameter tube. As the number of turns increases, the inductance L of the resulting solenoid increases, and so does the resistance R of the wire because its length increases.

(a) Write an expression for the characteristic time τ = L/R of the solenoid in terms of the wire diameter d, the number of turns N, the solenoid diameter D, and the resistivity r of copper (Table 21-1).

(b) If N increases, will τ increase, decrease, or remain the same?

(c) Find t for N = 325 turns.