AP Physics C - Free Response Questions involving Inductance and Capacitance (for Practice)

In the post dated 23-12-2007 a free response question on inductance was discussed. You can access that question along with other questions related to inductance by clicking on the label ‘inductance’ below this post. The circuit pertaining to the question referred to above is shown in the figure.

Let us modify the question to facilitate more practice. Here are two questions:

(1) In the circuit shown, the battery and the inductor have negligible resistance. The currents through R₁, R₂ and R₃ are i₁, i₂ and i₃ respectively when the switch S is kept closed. The switch S is closed at time t = 0.

(a) Calculate the potential difference across the 8 Ω resistor R₂ immediately after closing the switch S.

(b) If the inductance is replaced by an uncharged 10 μF capacitor what will be the potential difference across the 8 Ω resistor R₂ immediately after closing the switch S? Justify your answer.

(c) After reaching steady state, in case (b) what will be the potential difference across the resistor R₂? Justify your answer.

(d) If a 16 Ω resistor is used instead of the capacitor mentioned in (b), calculate the current through R₂ immediately after closing the switch S.

(e) Show the nature of variation of the potential difference across R₂ with time t in cases (b) and (d).

(2) In the above circuit, suppose the switch S was closed for sufficiently long time so that steady state was reached. In this steady state the switch S is opened at time t = 0.

(a) Will there be any change in the directions of the currents i₂ and i₃ on opening the switch S? Put a tick mark against the correct option among the following:

No change____

Current i₂ alone is reversed____

Current i₃ alone is reversed____

Both i₂ and i₃ are reversed____

Justify your answer.

(b) Calculate the potential difference across resistance R₂ immediately after opening the switch S.

(c) Calculate the total amount of heat generated in resistance R₂ after switch S is opened.

(d) Calculate the power dissipated in resistance R₂ in the steady state, before opening the switch S.

Try to answer the above two questions which carry 15 points each. You can take about 15 minutes for answering each question.

I’ll be back shortly with model answers for your benefit.