Qualitative/quantitative translation (QQT)
Comparing two LC oscillators
- Unit 13
- 8 points
- About 18 minutes
You can use a calculator on this question, just like on exam day.
A shorter multipart problem that connects reasoning in words with an equation. You make and justify a claim without equations, derive an equation from a physics principle, and then explain whether the two agree or use them to predict what happens in a changed situation. On the exam: Question 4 of 4. Section II has 4 questions in 95 minutes (50% of the exam score), one of each type in this order; calculator and equation sheet allowed. The CED suggests 15–20 minutes.
The question
In circuit 1, a capacitor of capacitance C is charged to a potential difference V₀, disconnected from the battery, and then, at t = 0, connected across an inductor of inductance L. The wires and inductor have negligible resistance, so the charge oscillates. Circuit 2 is identical except that its capacitor has capacitance 4C. It is also charged to V₀ before being connected to an identical inductor.
Suggested time: 18 minutes
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Part (a)
3 points(i) Is the maximum current in circuit 2 greater than, less than, or equal to the maximum current in circuit 1? (ii) Is the period of oscillation of circuit 2 greater than, less than, or equal to that of circuit 1? Justify your answers. Do not use equations in this part; reason in words.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
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Part (b)
3 pointsDerive expressions for the maximum current and the period of oscillation of circuit 1, in terms of C, L, and V₀, and use them to find the ratio of each quantity for circuit 2 to the same quantity for circuit 1.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (c)
2 pointsExplain how your expressions from part (b) agree with your reasoning in part (a).
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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