Two solenoids,wound from wire from the same spool,have the same length and cross-sectional area,but solenoid №1 has half the turns of solenoid №2.If these solenoids are each connected to a circuit,and the only non-negligible resistance is that of the solenoids,which solenoid gives the greater time constant and by what factor?
A) №1 by a factor of 2
B) №2 by a factor of 2
C) №2 by a factor of 4
D) No answer above is completely correct.

Question

Quizplus · Accepted Answer

The time constant, τ, of an RL circuit is given by τ = L/R, where L is the inductance and R is the resistance. Since the two solenoids have the same length and cross-sectional area, their inductances will be proportional to the number of turns, so L1/L2 = 1/2. However, the resistance of solenoid №1 will be half of that of solenoid №2, since resistance is proportional to length but inversely proportional to cross-sectional area, so R1/R2 = (1/2)/(1) = 1/2. Therefore, the time constant τ1 and τ2 for solenoid №1 and solenoid №2, respectively, are:
τ1 = L1/R1 = (1/2)L2/(1/2)R2 = L2/R2 = 2τ2
This shows that solenoid №2 has the greater time constant by a factor of 2, so the correct answer is B.

Two Solenoids,wound from Wire from the Same Spool,have the Same