Translation between representations (TBR)
Sharing charge between two capacitors
- Units 10 and 11
- 12 points
- About 28 minutes
You can use a calculator on this question, just like on exam day.
A multipart problem about one situation shown in several ways. You draw a diagram, derive equations, sketch or draw graphs, and then explain whether your answers agree with each other or use them to predict what happens when the situation changes. On the exam: Question 2 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 25–30 minutes.
The question
Capacitor 1, with capacitance C, is charged to a potential difference V₀ and then disconnected from its source. At time t = 0, a switch is closed to connect it in a single loop with an uncharged capacitor 2, with capacitance 2C, and a resistor of resistance R. The positive plate of capacitor 1 connects through the resistor to one plate of capacitor 2, and the other two plates are connected by a wire.
Suggested time: 28 minutes
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Part (a)
2 pointsDerive expressions for the final charge on each capacitor and the final potential difference across each, a long time after the switch is closed.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (b)
1 pointDerive an expression for the current in the resistor immediately after the switch is closed.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (c)
3 pointsLet q be the charge on capacitor 2 at time t. Starting with Kirchhoff’s loop rule, derive an expression for the current I in the resistor as a function of time.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (d)
3 pointsYou can’t draw here, so describe the two graphs you would sketch on separate axes, from t = 0 until long after the switch is closed: (i) the current I as a function of time, and (ii) the charge q on capacitor 2 as a function of time. Give the starting and final values and show what happens at one time constant.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (e)
2 pointsDerive an expression for the total energy dissipated in the resistor, in terms of C and V₀.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (f)
1 pointA student claims that using a resistor with a smaller resistance would reduce the energy dissipated. Do you agree or disagree? Justify your answer.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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