activity, which is about drawing a circuit on the board. It is important just
direct students and not to help them do it. Teacher can remind them the basic
elements/symbols of the circuit components. Aim of this activity is focus
students attention on the lesson and interest them to know more about X
element. In this demo teacher uses a capacitor, power supply/battery,
voltmeter, switch, a light bulb and a tablet. The graph of V(t) can be seen on
the screen if sensors are used. If there is no access to the internet teacher
can use phet colarado simulation (file-capacitor-lab_en).Before using this
virtual simulation teacher should set up Java program on a computer.
More able students
will be given an extended theory about capacitance in parallel and series
connections (Attachment 1). This can be given to those students who have
already investigated capacitance relationship with the distance between plates
and the area. As an extra task some students can analyze and solve problems on
attachment 2 and compare their answers with the mark scheme.
parallel and in series not covered in this topic according to the Course plan
for Grade 10 (Учебный
план для 10 кл ОГН). However, teacher might deduce the equation for the
equivalent capacitor in series and parallel and solve some problems with the
whole class. Teacher might differentiate this task, so students that are more
able can investigate this issue.
1 Capacitors in series and in parallel
Attachment 2 Problems with solution on
topic Capacitor and capacitance
solving. When solving problems, students follow the rule. Before proceeding to
the next task, verify the solution with two neighbors.
the charge accumulated by the capacitor on each plate of a 4.0 x 10-6
F capacitor when it is connected to a battery with a voltage of 12 V.
;q =48 mC
The distance between the plates of a flat capacitor 2.0 x10-3 m,
determine the area of the plates, if the capacitor has a capacity of 1.0 nF.
;S = 0,225 m2
the voltage of the battery to which the capacitor is connected. The plate
having an area of each plate is 2.0 cm2 and with a distance between
the plates of 2 mm if the charge accumulated by the capacitor is 4.0 pC.
= 4.5 V
area of each plate of a flat capacitor is 520 cm2. At what distance
from each other should the plates be positioned so that the capacitance of the
capacitor is 46 pF? Between the plates is leaf mica. The dielectric constant of
mica is 7.
; d = 7 cm
conceptual questions and problems:
Can we obtain two pieces of oppositely charged material when we place in the
outer electric field
a piece of metal
a piece of polystyrene? Explain.
What will you observe when a piece of metal is placed into the electric field?
Is there any attraction or repulsion?
What if you do the same with a piece of insulator? Is it the same or not? What
is the difference?
Estimate the value of resultant electric field strength inside a conductor or
insulator of relative permittivity 4 and finish the graphs
10 µF capacitor is connected to a 50 V supply. Calculate the charge and energy
stored on the capacitor.
a.What is the capacitance of an empty parallel-plate capacitor with
metal plates that each have an area of 1.00m21.00m2, separated by 1.00 mm?
b.How much charge is stored in this capacitor if a voltage of 3.00×103V3.00×103V
is applied to it?
1. A 30 μF capacitor is connected to
a 9.0 V battery.
a Calculate the charge on the capacitor.
b How many excess electrons are there on
the negative plate of the capacitor? (Elementary charge e = 1.6 × 10–19
2. The p.d. across a capacitor is 3.0 V
and the charge on the capacitor is 150 nC. Determine the charge on the
capacitor when the p.d. is:
a 6.0 V  b 9.0 V.
3. A 1000 μF capacitor is charged to
a potential difference of 9.0 V. a Calculate the energy stored by the
capacitor.  b Determine the energy stored by the capacitor when the p.d.
across it is doubled.
4. For each circuit below, determine the
total capacitance of the circuit.
5. The diagram shows an electrical
Addidtional multilevel questions:Higher level
6. A 10 000μF capacitor is charged to
its maximum operating voltage of 32 V. The charged capacitor is discharged
through a filament lamp. The flash of light from the lamp lasts for 300 ms.
a. Calculate the energy stored by the
b. Determine the average power dissipated
in the filament lamp.
7. The diagram shows a 1000 μF
capacitor charged to a p.d. of 12 V. a Calculate the charge on the 1000 μF
b. The 1000μF capacitor is connected
across an uncharged 500μF capacitor by closing the switch S. The charge
initially stored by the 1000μF capacitor is now shared with the
500μF capacitor. i Calculate the total capacitance of the capacitors in
ii Show that the p.d. across each
capacitor is 8.0 V.
9 A 220 μF capacitor is charged to a
potential difference of 8.0 V and then discharged through a resistor of
resistance 1.2 MΩ. a Determine the time constant τ of the circuit.
b Calculate: i the initial current in the
circuit  ii the current in the circuit after a time equal to 2τ
iii the p.d. across the capacitor after a
time of 50 s.
Addidtional multilevel questions:Extension
10. A 100 μF capacitor is discharged
through a resistor of resistance 470 kΩ.
Determine the ‘half-life’ of this circuit.
(The half-life of the circuit is the time taken for the voltage across the
capacitor to decrease to 50% of its initial value.)
11. The diagram below shows a charged
capacitor of capacitance C. When the switch S is closed, this capacitor is
connected across the uncharged capacitor of capacitance 2C.
Calculate the percentage of energy lost as
heat in the resistor and explain why the actual resistance of the resistor is
47. Complete the following statement: When a
dielectric with constant k is
inserted between the plates of a charged isolated capacitor
(a) the capacitance is reduced by a
(b) the charge on the plates is reduced by
a factor of k.
(c) the charge on the plates is increased
by a factor of k.
(d) the electric field between
the plates is reduced by a factor of k.
(e) the potential difference between the
plates is increased by a factor of k.
48. A parallel plate capacitor has a potential
difference between its plates of 1.2 V and a plate separation distance of 2.0
mm. What is the magnitude of the electric field if a material that has a
dielectric constant of 3.3 is inserted between the plates?
(a) 75 V/m (c) 250
V/m (e) 500 V/m
(b) 180 V/m (d) 400
49. A capacitor has a very large capacitance of 10 F.
The capacitor is charged by placing a potential difference of 2 V between its
plates. How much energy is stored in the capacitor?
(a) 2000 J (c) 100
J (e) 20 J
(b) 500 J (d) 40
50. The effective area of each plate of a parallel
plate capacitor is 2.4 m2. The capacitor is filled with neoprene
rubber (k =
6.4). When a 3.0-V potential
difference exists across the plates of the capacitor, the capacitor stores 5.0
µC of charge. Determine the plate separation of the capacitor.
(a) 7.2 ´ 10–5 m (c) 1.7 ´ 10–4 m (e) 8.2 ´ 10–5 m
(b) 3.0 ´ 10–4 m (d) 5.3 ´ 10–4 m
51. A uniform electric field of 8 V/m exists between
the plates of a parallel plate capacitor. How much work is required to move a
+20 mC point charge from the negative plate to
the positive plate if the plate separation is 0.050 m?
(a) 0.4 J (c) 8
´ 10–4 J (e) 8 ´ 10–6 J
(b) 1.6 J (d) 8
´ 10–5 J
52. A capacitor is initially charged to 2 V. It is
then connected to a 4 V battery. What is the ratio of the final to the initial
energy stored in the capacitor?
(a) 2 (c) 6 (e) 10
(b) 4 (d) 8
53. A parallel plate capacitor has plates of area 2.0 ´ 10–3 m2 and plate
separation 1.0 ´ 10-4 m.
Determine the capacitance of this system if air
fills the volume between the plates.
(a) 1.1 ´ 10–10 F (c) 3.2 ´ 10–10 F (e) 5.3
´ 10–10 F
(b) 1.8 ´ 10–10 F (d) 4.4 ´ 10–10 F
54. A parallel plate capacitor has plates of area 2.0 ´ 10-3 m2 and plate separation 1.0 ´ 10-4 m.
Air fills the volume between the plates. What
potential difference is required to establish a
charge on the plates?
(a) 9.3 ´ 102 V (c) 1.7 ´ 104 V (e) 3.7 ´ 105 V
(b) 2.4 ´ 104 V (d) 6.9 ´ 103 V
55. A potential difference of 120 V is established
between two parallel metal plates. The magnitude of the charge on each plate
is 0.020 C. What is the capacitance of this capacitor?
The plates of a parallel plate capacitor each have an
area of 0.40 m2 and are separated by a distance of 0.02 m. They are
charged until the potential difference between the plates is 3000 V. The
charged capacitor is then isolated.
56. Determine the magnitude of the electric field
between the capacitor plates.
(a) 60 V/m (c) 1.0
´ 105 V/m (e) 3.0
´ 105 V/m
(b) 120 V/m (d) 1.5 ´ 105 V/m
57. Determine the value of the capacitance.
(a) 9.0 ´ 10-11 F (c) 3.6 ´ 10-10 F (e) 6.4
´ 10-10 F
(b) 1.8 ´ 10-10 F (d) 4.8 ´ 10-10 F
58. Determine the magnitude of the charge on either
(a) 1.8 ´ 10-7 C (c) 4.9 ´ 10-7 C (e) 6.8
´ 10-7 C
(b) 2.7 ´ 10-7 C (d) 5.4 ´ 10-7 C
59. How much work is required to move a –4.0 mC charge from the negative plate to the
positive plate of this system?
60. Suppose that a dielectric sheet is inserted to
completely fill the space between the plates and the potential difference
between the plates drops to 1000 V. What is the capacitance of the system
after the dielectric is inserted?
(a) 1.8 ´ 10-10 F (c) 5.4 ´ 10-10 F (e) 6.8
´ 10-10 F
(b) 2.7 ´ 10-10 F (d) 6.2´ 10-10 F
61. Suppose that a dielectric sheet is inserted to
completely fill the space between the plates and the
potential difference between the plates drops to
1000 V. Determine the dielectric constant.