As shown in Figure2, a network of three resistors, aninductor, and a switch are

Question

As shown in Figure2, a network of three

resistors, aninductor, and a switch are

connected to abattery as shown in Figure 1.

a) The switch hasbeen disconnected for a

long time. At time t= 0, the switch is

closed. At thisinstant of time, calculate Figure 2.

all the currents inthe network and the

voltages across allresistors.

b) After a longtime, all currents reach a steady state. Recalculate allthe

currents in thenetwork and the voltages across all resistors.

Hint: Take note of the value of the steady statecurrent through the inductor, as you

will need it insteps c) and d), below

c) The clock isreset, and at time t = 0 the switch is again opened. Calculate thevalue of

the voltage acrossthe inductor at time t = 0.125 sec. Indicate whether pointa or

pointb is at a higher potential.

Hint: Current I2 through the 4 resistor instantaneously reverses and assumesthe

value ofI3.

d) How long does ittake the current through the inductor to fall to 1% of the valueit

had at the instant the switch wasopened in part c)?

Explanation / Answer

b) after very long time when it reaches steady state theinductor shall behave as a short thus current I1= 10/(4+4/3) =30/16 or 15/8 = 1.875 A , I2=1.875*2/3 = 1.25 A , I3 = .725 A
c) after reversing the switch it becomes an R L circuit with i= .725 * e^-t/12 just substituting the value of t= 0.125 shouldgive the result
d) the value falls 1% when .00725 = .725* e^-t/12 or the valueof t can be directly evaluated

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