Question

A 57.0 m length of insulated copper wire is wound to form a solenoid of radius 2.1 cm. The copper wire has a radius of 0.51 mm. (Assume the resistivity of copper is

ρ = 1.7 ✕ 10⁻⁸ Ω · m.)

(a) If the solenoid is attached to a battery with an emf of 6.0 V and internal resistance of 350 mΩ, compute the time constant of the circuit.
____________ms

(b) How long would it take to reach 99.9% of its maximum current?
____________ms

(c) What maximum energy is stored in the inductor?
____________mJ

Answer 1

02 = length of wire =57m ri, solenoida 2.1x102m 0.51 x 10-3m e = 1+7x10-8 sm of wire R= p = 1.7X70-8x_57 z (0.51X10-372 R = 1.180 R a) Resistance now, number of turns 57 L No arri 22.2.1x 10-2 N=432 turs length of solenoid, != N(282) = 432* 2x 0.518103) l'= 0.441m self Inductance, Yo N²282 l' unx107432)** 314%(2. 1x 10?) 0.44 7.36*10-44 LE

time constant, TE Rew 736x104 1:186 + 0.35 = 4.792 x 10-4 sec (0.4792.ms now, maximumum current v Rto 6 m 1.186 70.35 = 3.91A Giren I= 0.999 Im sam 0. aaq If = mm Cicek) -t In (0.001) 4.79x10-y t= 3.31X10-3 3.31 msee maximum energy E = £ L 12 1x7.36*10mly (3.9112 5.63 X10-31 - 563 J