The switch in the circuit shown in Fig. 32-31 has been closed for a long time. F

Question

The switch in the circuit shown in Fig. 32-31 has been closed for a long time.

Figure 32-31
http://www.webassign.net/fgt/fgt3_32-31alt.gif

(a) If E = 11 V, R1 = 4000 ohms, and R2 = 27 ohms, what is the current (magnitude and direction) in each leg of the circuit?
I1 =________mA down
I2 =__ 0___ mA no current
IL= ____________mA right
(I1 and IL should be the same value)
(b) When the switch is opened, the current in the inductor drops by a factor of 2 in 9.3 µs. What is the value of the inductance?
____________ mH

(c) What is the current (magnitude and direction) passing in each leg at 14 µs?
I1= ___0_____mA no current
I2=__________mA left
IL=__________mA right
(I2 and IL should be the same value)

Explanation / Answer

a)

I1 = IL = /R1 = 11/4000 = 2.75 mA

I1 = 2.75 mA down
I2 = 0 mA no current
IL= 2.75 mA right

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b)
i(t)/i = e^(-Rt/L)

1/2 = e^(-27*9.3*10^-6/L)

>>>> L = (-27*9.3*10^-6)/ln0.5

           = 0.36226 mH

----------------------------------------------

c)

i(14s) = {e^(-27*0.014/0.36226)} * i = 0.352 * 2.75 = 0.968 mA

I2 = IL = 0.968 mA

I1= 0 mA no current
I2= 0.968 mA left
IL= 0.968 mA right

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