Question

A 12.0 V battery is connected into a series circuit containing a 20.0 Ω resistor and a 2.70 H inductor.

(a)

In what time interval (in s) will the current reach 50.0% of its final value?

s

(b)

In what time interval (in s) will the current reach 90.0% of its final value?

s

What If? After a very long time, using a switch like that shown in the figure below, the battery is removed and the inductor is connected directly across the resistor.

The circuit is a rectangular loop with a vertical wire in the middle that extends from the bottom side of the loop to almost reach the top side, ending at point b below the top side. The left side contains, from top to bottom, a switch S₁ and a battery of emf ℰ with the positive terminal above the negative terminal. Switch S₁ is open. The right side contains an inductor of inductance L. The top side, from left to right, contains point a, a switch S₂ and a resistor of resistance R. In the figure, switch S₂ is in contact with point a.

(c)

In what time interval (in s) will the current decrease to 50.0% of its initial value?

s

(d)

In what time interval (in s) will the current decrease to 10.0% of its initial value?

s

Answer 1

@ it)= (-25) Imax = F 0.5E = E - ete) 0.5-1 = - et e ls (0.5 = -t & =-2.7 l. (0.5) = 0.09365 t = -1/2 ls (0.5 20 = 0.3108S (6 ls (0.9) = -t e t = -ls (0.9 x 2.7 @ alt) = Inax ett alt) = & et e max -tR -tR 0.5 = e ti lo (0:5)= -tĘ = 0.0936 S An (6.5) 2.7 20 tR o.1 E R R = e i te o. = e ln (0.1) = - I E = 0.3108 s t = -de (0.1) 2.7 20