PHYSICS, SECTION D (1/2) – ELECTROSTATICS AND CIRCUITS
STATIC ELECTRICITY AND ATTRACTION
Electrostatics is the study of charges at rest. When two insulators are rubbed together, they can
produce electrostatic attraction. Matter is made of atoms which have negatively charged
particles called ELECTRONS orbiting around a small nucleus.
In the normal state, the atom has an equal number of electrons and protons, therefore we say that
it is electrically balanced or uncharged. At times, when rubbing a surface, electrons are removed
from the orbit and the object becomes POSITIVELY charged. The object that the electrons
rubbed off on then become NEGATIVELY charged.
It should be noted that only the electrons will move
because they are much lighter than protons. Protons are
also bound to the nucleus, which make them unlikely to
move due to friction.
If a plastic rod was used, it would gain electrons instead.
Note the formula for charge: Q = It
Q = Charge (C)
I = Current (A)
t = time (s)
Charge is measured in COULOMBS. One coulomb is equivalent to 6.25 x 1018 electrons. Devices
that store charge are called CAPACITORS. and gain current as time passes. It should be noted
that time plays a major factor in terms of charge.
Example questions: 1. During a certain lightning strike, a current of 5 x 104 A flows for a time
period of 0.15 ms. Calculate the quantity of charge of the lightning strike.
Q = It
= (5 x 104) x (0.15 x 10-3) = 7.5C
2. The makers of a cellphone have upgraded its battery capacity from 4320C to 9000C. If a
charger delivers 0.6A, how much more time will it take to charge the new battery than the old?
ΔQ = 9000 – 4320 = 4680 C
Δt = ΔQ ÷ I = 4680 ÷ 0.6
= 7800 s (or 130 mins)
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POTENTIAL DIFFERENCE
kinetic energy based on differences in height
(such as a river flowing downstream),
p.d. refers to the energy that generates an
e.m.f. (electromotive force), allowing
charges to flow to a component.
Potential difference (or p.d.) is simply
another term for voltage. Similar to how
gravitational potential may convert to
For e.g. the laptop has to have a lower p.d.
than the solar cell for the charges to flow
from the solar cell to the laptop. If the laptop
had a higher p.d. than the solar cell, the
laptop would charge the solar cell instead.
CHARGING BY INDUCTION
Objects can also be charged by placing them next to each other and using a charged rod within
proximity. This method is called charging by INDUCTION.
Examples of technology that employ electrostatic forces are: PHOTOCOPYING MACHINES,
ELECTROSTATIC PAINTING, ELECTROSTATIC SMOKE PRECIPITATORS.
ELECTRIC FIELDS
An electric field is defined as a region around a charged particle or object within which a force
would be exerted on other charged particles or objects.
Electric fields flow outward from
+ve charges and inward from –ve
charges.
So they always flow from positive
to negative.
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CIRCUIT COMPONENTS
Component
Circuit Symbol
Note
Dry cell / Battery
Converts chemical to electrical energy.
Switch
Controls paths of electron flow.
Fixed Resistor
Decreases current, value is constant.
Variable Resistor (rheostat)
Decreases current, value can adjust.
Bulb / Lamp
Converts electricity to light + heat.
Voltmeter
Measures voltage. Connected in parallel.
Ammeter
Measures current. Connected in series.
Fuse
Breaks circuit path if current is too high
Semiconductor diode
Converts a.c. voltage to d.c. voltage.
a.c. Power Source
Typically a power outlet.
Motor
Converts electrical to mechanical energy.
Transformer
Alters voltage by altering current.
Galvanometer
Deflects needle due to small currents.
Heater
Generates thermal energy.
Bell
Releases sound energy.
Thermistor
Resistance reduces when temperature
increases.
Photoresistor / LDR
(Light-Dependent Resistor)
Resistance reduces when light intensity
increases.
LED (Light-Emitting
Semiconductor light source. Releases
Diode)
photons. Very efficient.
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WHAT IS THE DIFFERENCE BETWEEN CURRENT AND VOLTAGE?
Quantity
Definition
Unit
Derivation of Unit
Voltage
The amount of energy per unit charge.
Volt (V)
1V = 1 J/C
Current
The amount of coulombs passing a point per
second.
Ampere
(A)
1A = 1 C/s
Resistance
A measure in the opposition of the flow of
current.
Ohm
(Ω)
1Ω = 1 V/A
The general formula that links each quantity above is:
This is also called OHM’S LAW, which states that
THE CURRENT THROUGH A CONDUCTOR BETWEEN TWO POINTS IS DIRECTLY
PROPORTIONAL TO VOLTAGE AND INVERSELY PROPORTIONAL TO RESISTANCE.
Measuring Voltage and Current
Instrument
Measures
How it is hooked up
Why?
AMMETER
Current.
IN SERIES
It has a very low resistance, so as
to not affect the circuit.
VOLTMETER
Voltage.
GALVANOMETER Direction of small
amounts of
IN PARALLEL
It has a high resistance, which
could affect the circuit in series.
Same as ammeter.
Same as ammeter.
current.
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WIRES AND RESISTANCE
Factor
Explanation
LENGTH
Long wires have higher resistances than shorter ones. More power loss
tends to occur along far distances. Electrical energy converts to heat.
THICKNESS
Wires of thick diameter have more conducting material and thus can
transfer more current. The thicker the wire, the lower the resistance.
CONDUCTOR
Wires made of good conducting material, e.g. copper have low resistance.
DIRECT AND ALTERNATING CURRENT
Alternating current is specific type of
electric current in which the direction of the
current's flow is REVERSED on a regular
An a.c. voltage can be converted to d.c.
voltage using a SEMICONDUCTOR
DIODE or RECTIFIER.
basis. The magnitude of the voltage
produced FLUCTUATES a.c. voltages are
found in:
Power lines, transformers, power outlets
Direct current is simply when it flows in
ONE DIRECTION at all times. It has a
FIXED magnitude. d.c. voltages are found
in: Cell phone battery, laptop battery, simple
electromagnet, hybrid vehicles
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PRIMARY AND SECONDARY BATTERY CELLS
Batteries can be divided in two categories: primary cells and secondary cells.
Characteristic
Primary cell (Dry Cell)
Secondary cell (Wet Cell)
Rechargeability
Absent.
Present.
Portability
High (small size)
Low (usually larger size)
Terminal Voltage
Lower (e.g. AA = 1.5V)
Higher (e.g. Car = 12V)
Internal Resistance
Higher
Lower
Structure
Zinc anode, carbon cathode,
contains a powder or paste
of MnO2.
Sulphuric acid electrolyte
with lead plates. Or lithiumion batteries. Liquid
electrolyte.
RECHARGING A BATTERY CELL
Secondary batteries (which are d.c.) are
recharged when they are connected to a.c.
supplies (such as outlets).
A TRANSFORMER steps down the voltage
from the outlet and a RECTIFIER converts
the a.c. voltage to d.c to flow into the battery
and be stored.
VI-GRAPHS
Components that obey the relationship given by Ohm’s Law are said to be OHMIC while components
that don’t, such as filaments lamps and diodes are said to be NON-OHMIC.
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DETERMINING RESISTANCE OF AN UNKNOWN RESISTOR, R
The apparatus is set up as shown in both methods with the ammeter in series with the resistor and
the voltmeter in parallel. However, the methods differ when it comes to obtaining different values
of current. In Method 1, the length of the resistance wire ‘d’ is varied by connecting the contact at
different points (recall that longer wires have higher resistance). In Method 2, a rheostat is used to
vary the resistance to obtain different values.
Using the setup in Method 2, a student obtained the following results. Plot a graph of V vs. I, and
find the gradient. What does the gradient represent?
V/V
2.00
3.00
4.00
5.00
6.00
I/A
0.42
0.60
0.84
1.02
1.18
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SERIES & PARALLEL CIRCUITS
Let’s analyse the simple series circuit below to state its characteristics:
If one component stops
working in a series circuit,
the circuit breaks and
current cannot travel to the
other parts in the circuit.
This is due to there being
only one pathway.
RESISTANCE IN A SERIES CIRCUIT – The total resistance in series is the sum of all
resistors in the circuit. For example, find the total resistance of a circuit which has two resistors of
10Ω and 15Ω.
FORMULA: RS = R1 + R2 ...
CALCULATION: RS = 10 + 15 = 25 Ω
CURRENT IN A SERIES CIRCUIT – The current flowing into each component in a series
circuit is equal to the current flowing out of each component. This means that each ammeter (A 1,
A2 and A3) would have the same reading. Show the calculation:
I = V/R
= 6/25 = 0.24 A
Note: Ammeters are placed in series next to the component to be observed. They have very low
resistance, so as to avoid significant alteration of the current passing through it in series.
VOLTAGE IN A SERIES CIRCUIT – The sum of the voltages of the individual components
in the circuit should equal the voltage of the power source. This means that the sum of voltages in
R1 and R2 should be equal to 6V. What are the voltages in R1 and R2?
V (R1) => V = IR
V (R2) => V = IR
= 0.24 x 10 = 2.4V
= 0.24 x 15 = 3.6V
Now recall that total voltage = 2.4 + 3.6 = 6V
Note: Voltmeters are connected in parallel to the components. They have very high resistance, so
only very small amounts of current pass through it, since voltmeters are on separate wire paths.
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Now, let’s analyse a simple parallel circuit with the same components as before.
Houses are wired in parallel.
This is because the overall
resistance is lower than series.
Also, if one component ceases
to work, the circuit is not
broken like in series, due to
other electron pathways being
available.
RESISTANCE IN A PARALLEL CIRCUIT – The total resistance in a parallel circuit is smaller than
the value of the individual resistors.
FORMULA: 1/RP = 1/R1 + 1/R2 ...
CALCULATION:
VOLTAGE IN A PARALLEL CIRCUIT – The voltage in a parallel circuit is equal on each wire.
Therefore, on this circuit, the voltage on each wire would be 6V.
CURRENT IN A PARALLEL CIRCUIT – Since the wire splits at several junctions, so does the
conducting path for the electrons. This causes the current to decrease through these paths.
Therefore, since A1 and A4 are on the same pathway, their current will be equal.
However, A2 and A3 will have different currents. The sum of A2 and A3 = A1.
Calculate the currents through A2, A3 and then use those to find the current in A1.
For A1 → I = V/R = 6/10 = 0.6A
For A2 → I = V/R = 6/15 = 0.4A
Therefore, the total voltage → 0.6 + 0.4 = 1.0A
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COMBINING SERIES AND PARALLEL CIRCUITS
In the diagram, each resistor is 6Ω. A and B are in series with each other. C is parallel to both A and B.
And resistor D is series to A, B and C combined. To simplify the circuit, we need to reduce the number of
resistors by ‘fusing’ their values.
(a)(i) Calculate the total resistance of A and B.
RS = 6 + 6 = 12 Ω
(ii) Calculate the total resistance of A, B and C.
(iii) Calculate the total resistance of A, B, C and D.
RT = 4 + 6 = 10 Ω
(b) Calculate the total current in the circuit.
I = V/R
= 12/10 = 1.2A
(c) Calculate the voltage through C. (Keep in mind that resistor D draws voltage)
Finding voltage through D
V = IR
= 1.2 x 6 = 7.2V
Therefore Voltage through A, B and C would be:
V = 12 – 7.2 = 4.8V
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POTENTIAL DIVIDERS
From the diagram, calculate the value of Vout.
Rs = 1000 + 500 = 1500 Ω
I = V/R
= 12/1500 = 0.008A
Vout = IR = 0.008 x 500 = 4V
OR → 500/1500 x 12 = 4V
Potential dividers (or potentiometers) operate simply by splitting the voltage at various points
in a circuit. They usually involve some type of variable resistor or sensor-operated resistor. They
are widely used for adjusting voltages in appliance circuits. For e.g. a radio may only need 6V
from a 9V battery. The divider splits the voltage and allows 6V to flow as a Vout value.
ELECTRICAL HAZARDS, WIRING AND FUSES
Some metals melt easily at much lower temperatures than normal. These metals can be used to
make a SAFETY FUSE. If too much electricity flows through the fuse wire, it will get so heated
that it will melt. This will BREAK THE CIRCUIT and no more CURRENT can pass. If no fuse
is present and too much current passes, there can be a risk of an electrical fire.
Circuit breakers have the same purpose of a fuse. One main difference is that fuses must be
replaced, while circuit breakers don’t have to be. Fuses act faster than breakers, however.
If an 8A current is being delivered through the live wire, which fuse will be best? 2A, 5A or 10A?
There are three types of wires:
Type of Wire
Purpose
Colour
LIVE
Delivers electrical energy and high a.c. voltages to
appliances. Connects all switches and fuses.
BROWN (or red)
NEUTRAL
Carries current back to the supply. Has roughly zero
volts.
GREY (or blue)
EARTH or
GROUND
Deposits excess electrons from the circuit into the
ground. It is connected to the appliance frame or
casing, not mains.
GREENYELLOW
Three main electrical hazards are: 1. Damp wires 2. Broken insulation in wires 3. Short circuits
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Fuses and switches are always connected to
the live wire. There is a potential danger of
the live wire becoming loose and touching
the metal case of appliances.
Touching the metal casing can then result in
electrocution. However, the ground wire
will carry those excess electrons into the
ground, so the earth wire is always
connected to a case or frame.
ELECTRICITY GENERATION & CONSERVATION
1. BOILER – An external energy source (e.g. coal, biofuel, uranium) heats water into steam.
2. TURBINES – The steam provides mechanical energy for the turbines to spin.
3. GENERATOR – The turbines spin a generator, which is a large magnet that spins in a coil.
4. TRANSFORMER – Increases voltage for power line transmission, decreases for household.
Since we are dependent on non-renewable fossil fuels, we can do a number of things to
conserve them:
1. Switch off electrical appliances and lights when not in use.
2. Convert from incandescent to LED light bulbs.
3. Find alternative methods of transport (e.g. public transport, bicycles).
4. Employ alternative sources of energy (e.g. solar, wind, biofuels).
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PHYSICS, SECTION D (2/2) – ELECTROMAGNETIC COMPONENTS
MAGNETS
A magnet is a material that has a north and south pole that could either attract or repel other
magnets or magnetic materials. Magnetic materials, however, have no poles and cannot attract
others but can be attracted by a magnet.
Nature
Material
Application
Temporary Magnet
Permanent Magnet
Can be magnetized easily.
Retains its magnetism for a long time.
Iron, mu-metal
Steel, alnico
Electromagnets, transformers
Compass needles, décor magnets, metal detectors
Magnets create fields around them, as illustrated below.
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MAGNETIC INDUCTION
When a piece of unmagnetised magnetic material (such as IRON) touches or is brought near to
the pole of a permanent magnet, it is attracted to the magnet and becomes a magnet itself. In other
words, the material is said to have been magnetically induced. It should be noted that only 3
metals can be magnetized:
By wrapping a cylindrical coil or SOLENOID around an iron core and passing d.c. through it, the
iron core will become magnetized.
The electric field
creates a magnetic
field because they are
both part of the same
electromagnetic force.
They are 90o to each
other
DEMAGNETISING A MAGNET
Method
Explanation
HEATING
Molecules begin to vibrate so quickly that domains are rearranged and the
charges at the poles disappear.
HAMMERING
Physical force rearranges domains and polar charges disappear.
A.C. VOLTAGE
The a.c. causes some domains at the magnetic poles to switch directions.
If done long enough, the polar charges will be nullified.
RELAY CIRCUITS (ELECTRIC BELL)
A typical relay circuit contains a switch that is
electromagnetically operated.
1. When the current passes through the
electromagnets, they generate a magnetic field.
2. The soft iron armature is then attracted to the
electromagnet. It is pulled towards it, and the
hammer hits the gong.
3. At the same time, the contacts are broken in the
circuit, causing current flow to cease and the
magnetic field to be lost. This restarts the circuit,
causing the bell to ring in rapid successions.
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FLOW OF CHARGES & CONVENTIONAL CURRENT
Flow of charges is different from a metal
conductor and electrolyte. In an electrolyte
(a liquid conducting material), both positive
and negative ions can flow. It can also
occur in both directions.
However, in a metal conductor, only
negative charges flow (electron flow) and
only in one direction (-ve to +ve terminals).
There is one thing to note, however. While electrons indeed do move from –ve to +ve, tradition in
the field of Physics is to work the opposite way. Due to past limitations, we must assume that
flow is +ve to –ve instead. This system is called CONVENTIONAL CURRENT.
FORCES ON CURRENT-CARRYING WIRES
In the figure above, the thumb pointing
straight out represents the CURRENT
while the other four curved fingers
represent the MAGNETIC FIELD.
With this rule, the magnetic effect of a
current can be predicted.
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Fleming’s Left-Hand Rule is used to
predict the force (or thrust), magnetic field
and direction caused by a passing current. In
order for this interaction to occur, all three
must be perpendicular to each other.
First Finger = Field/Flux
SeCond Finger = Current
THumb = THrust
Force, magnetic field and current are linked
this way. If two are at a right angle, the third
can be produced.
•
Predict the direction of the wire in Fig 1. (downwards)
•
In Fig 2, the wire is being thrusted out of the page. Draw an arrow indicating the
conventional current direction, as well as the +ve and –ve terminals. (downwards)
APPLICATION OF LEFT HAND RULE TO A TURNING COIL
Predict whether the coil ABCD will have a clockwise or anticlockwise moment by determining
the forces on AB and CD.
Why would there be no force on BC?
In order to produce a thrust, the magnetic flux must be PERPENDICULAR to the current. At BC,
they are not perpendicular to each other, but parallel. There is no force as a result.
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D.C. MOTORS AND A.C. GENERATORS
Characteristics
d.c. motor
a.c. generator
Power source
Battery
External turning force
Energy conversion
Electrical → Mechanical
Mechanical → Electrical
Components
Split ring commutator
Slip rings
How to make the
Increase battery voltage.
motor spin faster or
Increase number of turns.
make the generator
create more power Use stronger magnets.
Increase turning force velocity.
Increase number of turns.
Use stronger magnets.
d.c. Motor: The purpose of the d.c. motor is to create a MOMENT on both sides of the wire
loops to create a turning force. This is due to Fleming’s Left Hand Rule, which says that in order
to create a force, a current must be PERPENDICULAR to the magnetic flux.
When the loop is turning, there is a chance the direction can reverse every half-rotation. A
SPLIT RING COMMUTATOR is used to BREAK THE CIRCUIT every half-turn to keep the
motor spinning in one constant direction. The direction of the turning force depends on the
orientation of the magnets and direction of conventional current.
a.c. Generator: It is noted that instead of a commutator, that SLIP RINGS are placed at the end
of the wire loop. The purpose of these is to allow the transfer of the alternating e.m.f. induced by
the rotating wire to the external circuit. Each one is connected to a contact brush, where it rotates
about the inner diameter. The faster the external rotator, more electrical energy can be converted.
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ELECTROMAGNETIC INDUCTION
Passing a magnet along a solenoid can allow electron flow and thus produce a VOLTAGE. This
is denoted by FARADAY’S LAW, which states that:
The voltage (or emf) induced in a coil is proportional to the rate of magnetic force
across it.
What this simply means is that the faster the magnet moves in and out of the coil, the more
voltage is obtained. If the magnetic field does not move, no voltage is induced.
Similarly, an alternating current constantly switches directions and by doing that, it inherently has
a changing magnetic field. An a.c. is therefore able to induce voltage across an adjacent coil.
A sensitive
galvanometer
is necessary to
detect very
small changes
in current.
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TRANSFORMERS
A transformer uses the concept of a constantly changing magnetic field to induce a voltage from a
primary to secondary coil. The more coils, the greater the electron flow and the higher the
voltage. However, if voltage is raised (step-up transformer), it trades by lowering the current.
Similarly, if voltage is lowered (step-down transformer), current is raised.
The following formulas are used in transformers:
Calculate the number of secondary coils and the secondary current in the primary coil.
Np/Vp = Ns/Vs
IpVp = IsVs
VsNp = VpNs
1000 x 5 = 200 x Ns
5000 = 200 Ns
Ns = 5000/200 = 25 turns
15 x 200 = Is x 1000
3000 = 1000 Is
Is = 3000/1000
= 3A
Due to the principle of conservation of energy, the power and energy output can never be more
than the input. In an IDEAL transformer, power input and output are said to be equal.
However, power loss does occur in transformers in real-world. To minimize power loss across a
wire, electrical energy is transferred with HIGH VOLTAGES and low currents. There are
numerous ways in which power loss can occur in a transformer, stated below:
Cause of Power Loss
Prevention Method
Line loss (heating)
Using wires of greater diameter.
Eddy currents
Laminating the soft iron core.
Hysteresis (delay during magnetization)
Using a perm-alloy core.
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LOGIC GATES
GATE
SYMBOL
NOT
TRUTH TABLE
EXAMPLE USE
Input
Output
1
0
0
1
Also called an inverter. It
may be used in circuits that
regulate factors, e.g. turning
on flash in cameras when
the environment is dark.
AND
OR
GATE
NAND
NOR
SYMBOL
Input 1
Input 2
Output
0
0
0
0
1
0
1
0
0
1
1
1
Input 1
Input 2
Output
0
0
0
0
1
1
1
0
1
1
1
1
TRUTH TABLE
An ATM will only allow a
user to access his account if
they swipe the correct card
and enters the correct PIN.
Doing one alone will deny
access.
If a machine is meant to
shut off if the temperature
OR pressure is too high, this
gate can allow the machine
to shut off if at least one
exceeds a certain limit.
EXPLANATION
Input 1
Input 2
Output
NAND = Opposite of AND
0
0
1
0
1
1
1
0
1
Also called the “universal
gate”, where the only zero
output is when there are two
zero inputs.
1
1
0
Input 1
Input 2
Output
NOR = Opposite of OR
0
0
1
The only positive output
0
1
1
0
0
0
occurs when there are two
1
1
0
zero inputs.
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Solve the following logic gate problems:
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An electric kettle is connected to an alarm that sounds whenever the kettle is switched on
and the lid is left open or the water level is below the heating element. The figure below
shows the circuit that controls the electric kettle’s alarm.
(a) Draw the appropriate logic gates in A, B and C to perform the electric kettle’s
alarm function. (A = AND, B = AND, C = OR)
(b) Complete the table below to show in which scenarios the alarm will go off or not.
Input
Output
L
M
N
X
Y
Z
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
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