please help me with each part of the question! LC ton.physics.ndsu.nodak.edu Con

Question

please help me with each part of the question!

LC ton.physics.ndsu.nodak.edu Consider an RL circuit as shown in the Figure with V 20 V, L-40 mH, and R-2300 ?. After the switch has been left open for a long time, the switch is closed att0. (a) What is the current the instant after the switch is closed? Submit Answer Tries 0/5 (b) What is the current a very long time after the switch is closed? Submit Answer Tries 0/5 (c) How long does it take the current in the circuit to reach 40% of its final (long time) value? Submit Answer Tries 0/5

Explanation / Answer

a) at the instant switch is closed the inductor acts as open circuit.

so, I = 0

b) after a long time current becomes maximum in the ckt.

Imax = V/R

= 20/2300

= 0.0087 A or 8.7 mA

c) time constant of the ckt, T = L/R = 40*10^-3/2300

= 1.74*10^-5 s

at time t, I = 40% of Imax

use,

I = Imax*(1 - e^(-t/T))

0.4*Imax = Imax*(1 - e^(-t/T))

0.4 = 1 - e^(-t/T)

e^(-t/T) = 1 - 0.4

e^(-t/T) = 0.6

-t/T = ln(0.6)

t = -T*ln(0.6)

= -1.74*10^-5*ln(0.6)

= 8.9*10^-6 s

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