6. -12 points Tipler6 28.P.067 My Notes Ask Your Teacher An inductor, two resist

Question

6. -12 points Tipler6 28.P.067 My Notes Ask Your Teacher An inductor, two resistors, a make-before-break switch, and a battery are connected as shown in the figure below. The switch throw has been at contact e for a long time and the current in the inductor is 2.7 A. Then, at t- 0, the throw is quickly moved to contact f.During the next 46 ms the current in the inductor drops to 1.5 A ey (a) What is the time constant for this circuit? ms (b) If the resistance R is equal to 0.44 , what is the value of the inductance L? mH eBook

Explanation / Answer

Io = 2.7 A

I = 1.5 A

t = 46 ms = 0.046 s

a) for the dischargning of the inductor

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

where T is the time constant

1.5 = 2.7 * e^(-0.046/T)

solving for T

T = 0.0782 s = 78.2 ms

the time constant is 78.2 ms

b)

NOw, as T = L/R

78.2 = L/.44

L = 34.4 mH

the inductance is 34.4 mH

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