An inductor and a resistor are connected with a double pole switch to a battery

Question

An inductor and a resistor are connected with a double pole switch to a battery as shown in the figure.

The switch has been in position b for a long period of time. A) If the switch is thrown from position b to position a (connecting the battery), how much time elapses before the current reaches 212 mA?

Answer in units of ms.

B) What is the maximum current in the inductor a long time after the switch is in position a?

Answer in units of A.

C) The switch has brushes within it so that the switch can be thrown from a to b without internal sparking. Now the switch is smoothly thrown from a to b, shorting the inductor and resistor.

How much time elapses before the current falls to 144 mA?

Answer in units of ms.

Explanation / Answer

R =5.86 ohms, L =129 mH, V = 8.7 V

(a) I =212 mA

from ohms law Vo = IoR

Io = 8.7/5.86 = 1.48464 A

Time constant T = L/R = 0.129/5.86 = 0.022 s

I = Io(1-e^-t/T)

0.212 = 1.48464(1-e(-t/0.022))

t =3.39 ms

(b) from ohms law Vo = IoR

Io = 8.7/5.86 = 1.48464 A

(c) I =144 mA

I = Io(e^-t/T)

0.144 = 1.48464(e^-t/0.022)

t = 51.33 ms

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