AP Physics C-Free Response Question on Inductance (for Practice)

In the circuit shown in the figure, the battery and the inductor have negligible resistance. The currents through R₁, R₂ and R₃ are i₁, i₂ and i₃ respectively. The switch S is closed at t = 0.

(a) Calculate the currents i₁, i₂ and i₃ immediately after closing the switch S(when t = 0).

(b) Calculate the currents i₁, i₂ and i₃ when steady state is reached.

(c) Show the nature of variation of the current through the battery graphically, with time ‘t’ on the X-axis and the current (i₁) on the Y-axis.

(d) What are the values of the slopes of the above graph at t = 0 and at t = ∞.

(e) The switch S is opened and the resistance R₃ is disconnected. If the switch S is now closed, what time is required for the current to attain 63.2% of the final steady value?

The above question carries 15 points. The division of points among the sections (a), (b), (c), (d) and (e) can be as 4 + 3 + 4 +2 +2. Try to answer the above question within 15 minutes or less. I’ll be back with the answer shortly.