The circuit shown contains two ideal AA batteries, several resistors and capacit

Question

The circuit shown contains two ideal AA batteries, several resistors and capacitors and an inductor of negligible resistance. The switch in the circuit has been open for a long time and all capacitors arc uncharged initially. For each switch position, find the current that flows through the 30Ohm resistor at t=0 (when the switch is first switched to that position). t=0.05 s, and t=infinity (after the switch has been in that position for a very long time, like 1 hr). You may find the following relationships for "charging" and "discharging" an inductor handy: I_charging(t) = I_max(1 -e_-t/t) I_discharging(t) = I_max e^-t/t

Explanation / Answer

For switch 1

Io = 3 / 53.75

    =   0.0558 A

     = 55.81 mA

=> I (0.05) = 55.81 mA

=> I (infinity) = 55.81 mA

For switch 2

Io = 0 mA

I (0.05) = 3/30 * (1 - e -0.05/0.00133)

              = 0.1 A = 100 mA

I (infinity) =   0.1 A   = 100 mA

For position 3

Io =   100 mA

I (infinity) = 0 mA

I (0.05) = 100 * e (-0.05/0.5)

              =   90.48 mA

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