Chapter 2 Capacitors
2005/2006
1. (a) Define the capacitance of a capacitor.
[1 mark]
(b) An air-filled capacitor consists of two parallel plates each with an area of 200 cm2,
separated by a distance of 0.4 cm.
(i)
(ii)
Calculate the capacitance of the capacitor. [Answer: 4.43×10-11F]
If a voltage source of 500V is connected to the capacitor, calculate the total
charge and the energy stored in the capacitor.
[Answer: Q = 2.22×10-8C, E = 5.55 × 10-6 J]
[9 marks]
2006/2007
2. (a)
FIGURE 1
FIGURE 1 shows two circuits, P and Q with identical capacitors but different resistors.
If RP is greater than RQ, which circuit will charge faster? Give your reasoning.
[3 marks]
(b) (i)
FIGURE 2
FIGURE 2 shows a circuit consisting of an air-filled parallel plate capacitor, D.C.
supply and lamp. When a sheet of glass is inserted between the plates of the
capacitor, explain the changes in lamp brightness.
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(ii)
FIGURE 3
Calculate the effective capacitance of the arrangement shown in FIGURE 3.
[Answer: 4µF]
[7 marks]
2007/2008
3. (a) A charged capacitor is connected in parallel to an identical capacitor which is uncharged.
State the changes in the potential difference, the effective capacitance and the total charge
on the combination of the capacitors.
[3 marks]
(b)
FIGURE 4
FIGURE 4 shows the variation of current in a circuit with time during a discharging
process of a capacitor through a resistor of 2 MΩ. Determine
(i)
the capacitance of the capacitor and the time constant τ.
[Answer: C = 2.5µF, τ = 5s ]
(ii)
the time taken for the current decreases to half of its maximum value.
[Answer: 3.46s ]
[7 marks]
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2008/2009
4. (a) (i)
(ii)
What is meant by 1 Farad?
Suggest ONE way to discharge a charged capacitor.
[2 marks]
(b) A capacitor of capacitance 20 µF is fully charged from a 50 V supply.
(i)
Calculate the amount of energy delivered. [Answer: 0.05 J ]
(ii)
Calculate the energy stored in the capacitor. Explain why there us a
difference between answer 4(b)(i) and 4(b)(ii). [Answer: 0.025 J ]
[ 8 marks]
2009/2010
5. A parallel-plate capacitor filled with air has plates of cross sectional area, A = 250 cm2
each and separation distance, d = 2.00 mm is connected to a battery 150 V.
(a) Calculate
(i)
the capacitance of the capacitor. [Answer: 111 pF ]
(ii)
the charge on each plate. [Answer: 1.66 × 10-8 C ]
[6 marks]
(b) The battery is then disconnected and a dielectric sheet is placed between the
plates. How does the energy stored in a capacitor change when the dielectric sheet
is inserted? Explain your answer.
[4 marks]
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2010/2011
6. (a) (i)
(ii)
Define capacitance.
Explain how a piece of dielectric inserted between the plates of a capacitor
will increase its capacitance.
[4 marks]
(b)
FIGURE 5
FIGURE 5 shows a 10 µF capacitor is charged through a 4 MΩ resistor using a 12
V battery when switch S is closed. The resistance of the microammeter is
negligible.
(i)
Calculate the maximum current in the circuit and sketch a graph of I
against t during the process. [Answer: 3 × 10-6 A]
(ii)
Determine the time constant. [Answer: 40s ]
[6 marks]
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2011/2012
7. (a) (i)
(ii)
State TWO differences between conductors and dielectrics.
The plates of a charged capacitor are conducted to a voltmeter. If the plates
of the capacitor are separated further, what happens to the reading
voltmeter? Explain your answer.
[5 marks]
(b) A capacitor stores 120 pC of charge when it is connected across a potential
difference of 24 V. Calculate
(i)
the capacitance of the capacitor. [Answer: 5 × 10-12F ]
(ii)
the amount of charge to be removed from the capacitor so that its potential
difference can be reduced to two-third of its initial value. [Answer: 40 pC ]
[5 marks]
2012/2013
8. (a) (i)
(ii)
What is meant by time constant?
Suggest TWO ways to increase the time constant.
[3 marks]
(b)
FIGURE 6
FIGURE 6 shows three capacitors connected to a 12 V battery.
(i)
(ii)
Determine the total capacitance of the circuit. [Answer: 6 µF ]
Calculate the charge stored in C3. [Answer: 2.4 × 10-5 C ]
[7marks]
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2013/2014
9. (a)
(i)
(ii)
Define dielectric constant.
2µF, 30µC
3µF
4µF
FIGURE 7
FIGURE 7 shows an arrangement of three capacitors, 2 µF, 3 µF
and 4 µF connected to a battery. If the charge on the 2 µF capacitor
is 30 µC, calculate the voltage across the 4 µF capacitor.
[Answer: 15 V]
[4 marks]
(b)
(i)
How to arrange two capacitors that will maximise the stored energy?
Explain your answer.
(ii)
A capacitor is discharging through a resistor. In terms of the time
constant τ, when will the charge decrease to half of its initial value?
[Answer: 0.69 τ s]
[6 marks]
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2014/2015
10.
(a)
(i)
Define capacitance.
(ii)
State TWO ways to increase the capacitance.
[3 marks]
(b)
A parallel plate capacitor is connected to a 6 V battery. The separation
distance between the plates is 0.06 cm and the area of the plates is
2.8×104 mm2.
(i)
Calculate the charge of the capacitor. [Answer: 2.5×10-9 C]
(ii)
If two other identical capacitors are connected in series to the
capacitor, calculate the effective capacitance.
[Answer: 1.4×10-10 F]
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