A 168-V battery, an inductor, and a 33 resistor are connected in series as shown

Question

A 168-V battery, an inductor, and a 33 resistor are connected in series as shown in the diagram below. A two-way switch makes it possible to include or exclude the battery. The switch that had been in position 1 long enough for the circuit to reach steady-state is then suddenly moved to position 2.

(a) What is the voltage across the resistor after the switch has been in position 2 for four time constants?

3.073 V <----correct

(b) At this same time, what is the magnitude of the current through the resistor?

Explanation / Answer

Current in a RL circuit is given by I = Io (1 - e-t/ ) where is the time constant

Io = V/R = 168 / 33 = 5.090909091 A (initial current)

after 4 time constant t = 4

I = I0  (1 - e-4 / ) = 5.090909091 ( 1 - e-4  ) = 4.997665 A

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