AP · AP C:E&M · free response
AP Physics C: Electricity and Magnetism · Question 9
AP Physics C: Electricity and Magnetism · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 13
- Topics
- 2
- Answer
- Complete
A student is given a capacitor of unknown capacitance, a resistor of known resistance R = 47 kΩ, a battery, a switch, a voltmeter of very high resistance and a stopwatch. The student wants to determine the capacitance.
- (a)
Describe Describe a procedure the student could use, and state which quantities should be recorded.
4 marks - (b)
Describe Describe how the student should linearise the data, and state what the slope of the resulting graph represents.
3 marks - (c)
Determine The student's graph of ln(V/V) against t has a slope of −0.43 s⁻¹. Determine the capacitance.
3 marks - (d)
Explain Explain why plotting ln V against t is preferable to determining the time constant by reading off the time at which V has fallen to 37% of its initial value.
3 marks
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(a)
Describe Describe a procedure the student could use, and state which quantities should be recorded.
Answer the command word directly and use precise physical vocabulary. Include only the distinct features or facts that earn marks, without burying them in unrelated background information.
- 1
1 point: charge the capacitor fully through the battery, then disconnect the battery and discharge it through the known resistor
- 2
1 point: record the voltmeter reading V at measured time intervals t from the start of the discharge
- 3
1 point: repeat the whole discharge several times and average the readings at each time
- 4
1 point: states why the voltmeter must have a very high resistance — otherwise it provides a parallel discharge path and shortens the time constant
(b)
Describe Describe how the student should linearise the data, and state what the slope of the resulting graph represents.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
1 point: V = V₀e^(−t/RC), so ln V = ln V₀ − t/(RC)
- 2
1 point: plot ln V on the vertical axis against t on the horizontal axis to obtain a straight line
- 3
1 point: the slope is −1/(RC), so C = −1/(R × slope)
(c)
Determine The student's graph of ln(V/V) against t has a slope of −0.43 s⁻¹. Determine the capacitance.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
1 point: RC = 1/0.43 = 2.33 s
- 2
1 point: C = 2.33 / 47 × 10³
- 3
1 point: C = 5.0 × 10⁻⁵ F (50 μF)
(d)
Explain Explain why plotting ln V against t is preferable to determining the time constant by reading off the time at which V has fallen to 37% of its initial value.
State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.
- 1
1 point: the single-point method relies on two readings only, V₀ and one other, so an error in either propagates directly into the answer
- 2
1 point: the graph uses every data point, so random errors average out and the slope is better determined
- 3
1 point: the straightness of the line is itself a test that the discharge really is exponential, which the single-point method assumes without checking
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