Two resistors, and inductor and a source of emf are connected with two switches

Question

Two resistors, and inductor and a source of emf are connected with two switches as shown in the figure below. Their values are R_1 = 4.00 KOhm, R_2 = 2.00 KOhm, L = 18.0 mH, and = 36.0 V. At time t = 0.0 mus switch S_1 is closed. a. What is the current in the circuit at t = 4.00 mus? b. After sufficient time for the current in the circuit to reach steady state value, switch S_1 is opened while switch S_2 is simultaneously closed. What is the current through the resistor R_2 10.0 mus after S_2 is closed?

Explanation / Answer

8)
a) Time constant of the ckt, T = L/(R1+R2)

= 0.018/(4000 + 2000)

= 3*10^-6 s or 3 micro s

Imax = V_battery/(R1+R2)

= 36/(4000 + 2000)

= 6*10^-3 A

at time t,

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

= 6*10^-3*(1 - e^(-4/3))

= 4.42*10^-3 A

b) Time constant of the ckt, T = L/R2

= 0.018/2000

= 9*10^-6 s or 9 micro s

at time t = 10 micro s,

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

= 6*10^-3*e^(-10/9)

= 1.98*10^-3 A

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