In the circuit below, we have L=20.78mH, R1=36.11kOhm, R2=94.04kOhm. The switch
ID: 2990082 • Letter: I
Question
In the circuit below, we have L=20.78mH, R1=36.11kOhm, R2=94.04kOhm. The switch is initially in position 1 (in this state, all currents and voltages are constant). At time t=0, the switch moves to position 2, causing the inductor to discharge. What is the discharging time constant tau? Express your answer in microseconds.
In the circuit below, we have L=20.78mH, R1=36.11kOhm, R2=94.04kOhm. The switch is initially in position 1 (in this state, all currents and voltages are constant). At time t=0, the switch moves to position 2, causing the inductor to discharge. What is the discharging time constant tau? Express your answer in microseconds.Explanation / Answer
before t=0, inductor acts as short circuit as there is no change in current and voltage.
=> current through R2 = 0
and current through inductor = current through the entire circuit= V / 1 KOhm
= 3/ 1 kOhm
= 3 mA
Now, when the switch is shifted to position 2, the inductor acts as current source and the current through it can't change suddenly,
so, now, R1 and R2 become parallel to each other with respect to the inductor as it acts as current source.
so the effective resistance = Reff = R1*R2 / (R1+R2)
= 43.686 kOhm
=> discharging time constant = L / Reff
= 34.8 mH / 43.686 kOhm
= 0.79659 micro seconds ans...