Download Nat 4-5 Unit 2 Section 1 pupil notes update Electrical Circuits

Turnbull High School
Physics Department
S3 Physics
Unit 2 :- Electricity and Energy
Section 1: Electrical Circuits
Name:
Class:
1
National 4
Unit 2: Section 1
By the end of Unit 2 section 1, I can:
• Draw and identify circuit symbols for an ammeter,
voltmeter, battery, resistor, variable resistor,
ohmmeter, switch and lamp.
• Identify simple series and parallel circuits
• Measure current, voltage and resistance using
appropriate meters in series and parallel circuits
• State that the voltage of a supply is a measure of
the energy given to the charges in a circuit.
• State that an increase in the resistance of a circuit
leads to a decrease in the current in that circuit.
• Draw circuit diagrams to show the correct positions
of an ammeter and voltmeter in a circuit.
• State that in a series circuit the current is the same
at all positions.
• State that the sum of the potential differences
across the components in series is equal to the
voltage of the supply.
• Carry out calculations involving the relationship
between potential difference, current and
resistance. (Ohms Law)
• Carry out experiments to investigate the factors
that affect resistance
• Describe the use of variable resistors and some
everyday applications for their use
2
National 5
Unit 2: Section 1
By the end of Unit 2 section 1, I can:
• Describe a simple model of the atom which includes
protons, neutrons and electrons.
• State that in an electric field a charged object
experiences a force.
• State that electrons are free to move in a
conductor.
• Describe electrical current in terms of the
movement of charges around a circuit.
• Carry out calculations involving the relationship
between charge, current and time.
• Distinguish between conductors and insulators and
give examples of each.
• Draw and identify circuit symbols for an ammeter,
voltmeter, battery, resistor, variable resistor,
ohmmeter, switch and lamp.
• Describe the differences between alternating and
direct current.
• State that the voltage of a supply is a measure of
the energy given to the charges in a circuit.
• State that an increase in the resistance of a circuit
leads to a decrease in the current in that circuit.
• Draw circuit diagrams to show the correct positions
of an ammeter and voltmeter in a circuit.
3
• State that in a series circuit the current is the same
at all positions.
• State that the sum of the potential differences
across the components in series is equal to the
voltage of the supply.
• State that the sum of the currents in parallel
branches is equal to the current from the supply.
• State that the potential difference across
components in parallel is the same for each
component.
• State that V/I for a resistor remains constant for
different currents provided the temperature of the
resistor remains constant.
• Carry out experiments to investigate the factors
that affect resistance
• Carry out calculations involving the relationship
between potential difference, current and
resistance. (Ohms Law)
• Carry out calculations involving resistors connected
in series and parallel.
Units, prefixes and scientific notation
1. Use SI units of all quantities appearing in the above
Content Statements.
2. Give answers to calculations to an appropriate number
of significant figures.
3. Check answers to calculations.
4. Use prefixes (µ, m, k, and M).
5. Use scientific notation.
4
A Simple Model of the Atom
Everything around us is made up of elements. Atoms are the
smallest possible particles that make up these elements.
Hydrogen, oxygen, copper, carbon and uranium are examples of
different elements. All the atoms of a particular element are
identical to each other and these are different from the atoms in
other elements.
The three main particles that make up an atom are called:
• electrons – n_ _ _ _ _ _ _ _ _ charged particles
• protons –
p_ _ _ _ _ _ _ _ _ charged particles
• neutrons – u_ _ _ _ _ _ _ _ _ particles.
We imagine the atom to look like the model shown below.
All atoms have a tiny central core called the nucleus.
The n _ _ _ _ _ _ contains both protons and n_ _ _ _ _ _ _ and is
p_ _ _ _ _ _ _ _ _ charged.
The negatively charged electrons orbit round this nucleus like
planets round the Sun.
5
In an uncharged (neutral) atom the number of protons in the
nucleus is e_ _ _ _ to the number of electrons orbiting the nucleus.
We sometimes have an even simpler model of the atom as shown
below.
electrons
Nucleus containing
protons and neutrons
Electrostatics is the study of objects which are electrically
charged.
6
Experiment 1: What is Electricity?
What you need: Two polythene (white) and two acetate
(clear) rods, watch glass, pieces of paper, cloth.
rubbed rod
rubbed rod
rubbed rod
Torn pieces of paper
watch glass
• Rub a polythene rod with a cloth and hold it over some small
pieces of paper - observe what happens.
• Rub two polythene rods with a cloth. Place one of them on the
watch glass and position the other so that both rubbed ends
are near each other - note the result.
• Repeat step 2 with two acetate rods and then with one
polythene and one acetate rod.
What happens when two charged polythene rods are
brought close to each other?
___________________________________________________
___________________________________________________
What happens when two charged acetate rods are brought close to
each other?
___________________________________________________
___________________________________________________
What happens when a charged polythene rod is brought close to a
charged acetate rod?
___________________________________________________
___________________________________________________
7
There are _______ types of charge. They are called
_____________ and _______________.
________ charges repel. ___________ charges attract.
The unit of charge is the ______________ (C).
The charge on an electron is _________________
Objects become charged due to a transfer of electrons (negative
charges).
(a) When an object gains electrons it becomes ________________
charged.
(b) When an object loses electrons it becomes ________________
charged.
Why learn about charge? (Uses of Electrostatics)
Printer/Photocopier
8
Electrostatic dust precipitators
Smoke is produced when fossil fuels burn. Smoke is made of tiny solid particles,
such as carbon. To remove these particles from the waste gases an
electrostatic precipitator is used.
1.Smoke particles pick up a negative charge.
2. Smoke particles are attracted to the collecting plates.
3. Collecting plates are knocked to remove the smoke particles.
Car Paint Spraying
Car manufacturers can save money by using
charged paint spray guns. They work because like
charges repel and unlike charges attract.
The spray gun is charged positively, which causes
every paint particle to become positively charged.
Like charges repel and the paint particles spread
out. The object to be painted is given a negative
charge and so attracts the paint particles. The
advantages of using this system are that less paint is wasted, the object
receives an even coat and the paint covers awkward ‘shadow’ surfaces that the
operator cannot see.
9
Electric Fields
When a small positive charge is placed near a charged
object, it is either attracted or repelled, and so it
experiences a force. The region surrounding the charged object,
where another charged object experiences a force, is called an
electric force field or simply an electric field.
A charged object cannot exert a force on itself as it cannot
experience it’s own electric field.
An electric field line is the line along which a small positive test
charge would move if free to do so. Electric field lines represent
the direction of the electrical force on a positive charge.
Note
1. The lines of force are continuous - starting on positive and
ending on negative charge.
2. The lines never touch or cross (like contours on a map).
3. The closer together the lines are, the stronger the electric field.
4. The arrows on the lines of force always point from positive to
negative i.e. they show the direction a positive charge would move
in if it were free to move.
Experiment 2: Electric Fields
Your teacher will demonstrate the Van de Graff Generator and
various types o electric fields using seeds and olive oil!
10
(a)
(b)
+
–
(c)
(d)
+
–
+
(e)
+
–
+
–
+
–
+
–
+
–
11
+
+
–
Uniform Electric Field - electric field is constant i.e. the force on
the charged object will be the same whatever it’s position in the
electric field.
In a uniform electric field, the lines of force are drawn equally
spaced and parallel to each other.
This means the field strength is constant. This is called a uniform
field.
Electric fields have certain similarities with gravitational fields.
12
Conductors
A material which is composed of atoms in which the outer
electrons are easily freed from the nucleus is called a conductor.
In our electrical work, we think of a model of a metal as being made
up as follows:
• Positively charged atoms (called ions) which are tightly bound
together to give the metal a fixed shape.
• Free electrons which are not attached to any particular ion but
can wander freely through the metal.
There are equal numbers of positive ions and free electrons so that
the metal is uncharged.
Positive Ion +
+
+
+
+
+
+
+
+
+
+
+
+
Free electron
The electrons are free to move but the ions are not.
electric field
+
+
+
+
+
+
+
+
+
+
+
+
movement of electrons
Under the action of an electric field, the free electrons will
experience a force moving them in one direction. In the diagram,
13
the direction of the electric field (the direction in which a positive
charge will move) is from left to right. Electrons (negative charges)
will be forced to the left (against the electric field direction) and
form an electric current. The electrons in a conductor are called
free charge carriers.
Tiny, negatively-charged particles called e _ _ _ _ _ _ _ _
flow around an electric circuit. E _ _ _ _ _ _ _ _ can only flow
through substances called c _ _ _ _ _ _ _ _ _ (e.g. m _ _ _ _ _)
but not through substances called i _ _ _ _ _ _ _ _ _ (e.g., most
non - m _ _ _ _ _, like p _ _ _ _ _ _ and r _ _ _ _ _ ).
The electrons lose their e _ _ _ _ _ _ _ _ _ energy as they flow
around an electric circuit. In the circuit above, the lamp converts
most of the e _ _ _ _ _ _ _ _ _ energy into l _ _ _ _ and
h _ _ _ energy.
14
Experiment 3:- Moving Charges
Your teacher will show you this experiment.
+
−
meter
meter
lamp
Van de Graaf
When the battery is connected to a lamp and an electrical meter,
the lamp lights and there is a reading on the meter i.e. there is an
E__________ C____________ in the circuit.
When the Van de Graaff generator is connected to the same meter,
and switched on, the reading on the meter shows that there is an
electric current. When the generator is switched off the reading on
the meter falls to zero and the dome of the generator is uncharged.
Charges must have moved through the meter.
The movement of charges (E___________) through a material is
called an electric current.
The above experiment shows that:
The longer (the time) an electric circuit is switched on, the greater
the number of charges transferred, and
The larger the (electric) current the greater the number of charges
transferred.
15
From the above, it can be shown that:
Charge transferred = Current x time of transfer
Q = I x t
coulombs (C)
This can also be written as
amperes (A)
seconds (s)
current = charge transferred
.
time taken
I = Q
T
• current = charge transferred in one second
Electric current is the charge transferred in one second.
One ampere is the current that is produced when one coulomb of
charge is transferred in one second.
1 ampere means that 1 coulomb of charge is transferred in one
second
i.e.
1 ampere = 1 coulomb per second
Q
I
t
16
To use a formula triangle do the following:
• cover up the symbol for the quantity that you are trying to
find
• if the remaining symbols are side by side – this means multiply
them
• if the remaining symbols are one over the other – this means
divide them.
From the formula triangle:
Q = I x t
I = Q
t
t = Q
I
Example 1: The current in a lamp is 2 A. How much charge
passes through the lamp in 30 s?
I=2A
t = 30 s
Q=?
Q=Ixt
= 2 x 30
Q = 60 C
Example 2 The charge transferred through a wire is 120 C. The
time taken to transfer the charge is 100 s. Calculate the current in
the wire.
Example 3: A charge of 2 C is transferred through a wire .The
current in the wire is 4 A. Calculate the time taken to transfer the
charge.
17
Experiment 4:- Conductors and insulators
What you need: power supply, lamp, selection of materials.
Set up the circuit shown below.
−
+
2V
lamp
X
Y
Complete the table by placing, in turn, each of the materials between
X and Y.
Material
Does lamp
light
Material
Plastic
Rubber
Copper
Nickel Silver
(n/silver)
Glass
Steel (s/steel)
Aluminium
Air
Wood
Paper
Coin
Iron
Does lamp
light
Materials can be divided into two groups called conductors and
insulators.
18
Materials that allow the lamp to light are called
______________.
Materials that do not allow the lamp to light are called _________.
In conductors (____________), the outermost electron of each
atom is free to wander from one atom to another. When a battery
is connected across a conductor these free electrons all move in
________ direction, forming an electric current.
In insulators (_________________), the outermost electrons of
each atom are tightly bound to the atom. There are no free
electrons available to form an electric current.
Circuit symbols
Circuit symbols are used in electrical circuits to represent circuit
components or devices. This makes them easier to draw and
understand. Some of the circuit symbols that you will need to know
are shown below.
−
+
battery
lamp
lead
resistor
variable resistor
fuse
switch
You will come across other symbols at other places in this Unit. You
must learn them!
19
Direct Current (d.c.) and Alternating Current (a.c.)
Electricity can be supplied in one of two forms - either d _ _ _ _ _ current
(d.c.) or a _ _ _ _ _ _ _ _ _ _ current (a.c.)
Your teacher will demonstrate to you the traces on an oscilloscope
produced by a battery and a mains electricity power supply
• Draw, in the boxes below, the traces observed on the screen
of the oscilloscope in each case.
Trace on oscilloscope
when using a battery
Trace on oscilloscope
when using a power supply
When a battery is connected to the oscilloscope, a ____________
line is obtained showing that the voltage is _____________. This
means that the electrons move in only ___________ direction i.e.
the current is in ________ direction. This is called a
____________ __________________ (d.c.).
d.c.
+
−
The direction of the current is always from negative to positive.
20
When the power supply is connected to the oscilloscope, a
____________ is obtained showing that the voltage varies in
______________ and ________________. This means that the
electrons move one way then the opposite way then back to the
first way and so on (clockwise, anticlockwise, clockwise,
anticlockwise and so on) i.e. the current is in one direction then in
the reverse direction.
This is called ____________________ __________________
(a.c.).
a.c.
The direction of the current is clockwise, then anti-clockwise, then
clockwise, then anti-clockwise and so on.
21
Alternating electrical supplies
When an a.c. source is connected to the oscilloscope, the
trace observed on the screen is wave like.
peak
1 cycle
One complete wave is called one cycle. The number of cycles
completed in one second is called the _________________.
_____________________ is measured in _________________
(______).
The mains electrical supply in the U.K. is an alternating supply
with a frequency of 50 Hz meaning that 50 cycles are completed
each second.
The peak voltage of an alternating supply is the maximum voltage it
can produce. An a.c. supply cannot produce this maximum or peak
voltage all of the time.
An average quantity called the quoted or effective value is used to
describe the voltage from an a.c. supply. This is the value that is
measured by an a.c. voltmeter.
22
Your teacher will demonstrate the following experiment
for you:
V
• Switch on the oscilloscope and set the Y gain control to 1 volt
per division.
• Adjust the output of the a.c. supply until the reading on the
voltmeter is as near to 1 V as you can get – record the value in
the table below.
• Measure the peak voltage on the oscilloscope screen – record
the value in the table below.
• Repeat for readings of 2 V and 3 V on the voltmeter.
Voltmeter
reading / V
Deflection of
trace / div
Peak voltage / V
The quoted or declared voltage of an a.c. supply (voltmeter reading)
is ________ ________ the peak voltage.
The quoted value of the mains voltage is 230 V but the peak value
is about 320 V.
23
Tutorial 1
1. Draw a simple model of an atom. Label a proton, nucleus,
neutron end an electron.
2. Draw the electric field pattern for the following charges:
(a)
+
(b)
-
(c)
+
3. A bulb draws a current of 0.5 A. How much charge flows
through it in 30 seconds?
12V
24
-
4. 646 C of charge flow though an electric heater in 150
seconds. What is the current in the heater?
5.
A current of 3·1 A flows through
an electric shaver for 4 minutes.
How much charge flows in this
time?
6. A 60 W bulb is switched on for 30 minutes. If 650 C pass
through it in this time, what is the current flowing in the
bulb?
25
7. A speaker system on a TV draws a current of 0·6 A. In an
average day 4 380 C of charge flows through the speaker
system. For how long is the TV switched on each day?
8. An electric kettle has a label on it as shown below.
MODEL No. 5510 - 01
capacity 1·7 litres
9·2 A /220 - 240 V
2·2 kW
After the kettle is switched on it will automatically switch off when
the water in it has boiled. On one occasion 1 656 C passed through
the kettle before it switched off. Use the information given to work
out how long the water took to boil?
9. An electric fire is rated
at 2.9 kW, 230 V, 12·5 A
How much charge will
flow through this fire in
a time of 3hours 320
minutes?
26
Experiment 5:- Types of circuit
What you need: power supply, 3 lamps.
+
6V
−
+
2V
−
A
B
A
B
C
C
Circuit 1
Circuit 2
Set
•
•
•
up circuit 1
Note the brightness of each lamp
Unscrew lamp A and observe what happens to lamps B and C
Screw in lamp A. Now unscrew lamp B – what happens to lamps
A and C?
• Screw in lamp B. Now unscrew lamp C – what happens to lamps
A and B?
Were the lamps very bright, bright or dim? __________.
When a lamp is removed (unscrewed), what happens to the other
lamps?____________________________________________.
How many paths can the current take in this circuit?__________.
What name is given to this circuit?________________________.
Set
•
•
•
up circuit 2
Note the brightness of each lamp
Unscrew lamp A and observe what happens to lamps B and C
Screw in lamp A. Now unscrew lamp B – what happens to lamps
A and C?
• Screw in lamp B. Now unscrew lamp C – what happens to lamps
A and B?
27
Were the lamps very bright, bright or dim? ________.
When a lamp is removed (unscrewed), what happens to the other
lamps?_____________________________________________.
How many paths can the current take in this circuit?___________.
What name is given to this circuit?_________________________.
In a ____________ circuit, there is only ________ path for the
current to take. If there is a gap in this type of circuit, there can
be no _______________.
In a ______________ circuit, there is _________ than one path
for the current to take. If there is a gap in this type of circuit,
there can still be ___________ paths for the current. The other
paths are called the ___________________ of the
________________ circuit.
28
Experiment 6(A):- Measuring current
Electric current is measured in A______________ (A) using an
A_____________.
Circuit symbol:
A
Your teacher will show you how to connect an ammeter in
a circuit
•
•
•
•
Set up the circuit.
Identify the point where the current is to be measured.
Make a gap in the circuit at this point.
Place the ammeter in the gap i.e. connect the ammeter in series
in the circuit.
• Make sure that the positive terminal (+) marked on the
ammeter is connected towards the positive terminal of the
power supply.
• If you obtain a negative reading on the ammeter, reverse the
connections on the ammeter.
−
+
X
−
+
X
−
+
X
29
+
A
Experiment 6(B):- Current in a Series Circuit
What you need: power supply, 3 lamps, an ammeter.
Set up the circuit as shown below. Check that all of the lamps are
lit.
A
B
D
C
−
6V
+
• Measure the current at positions A, B, C and D
• Complete the table
Position
Current / A
A
B
C
D
• How many paths can the charge take as it passes round the
circuit?________________________________________.
• What happens to the current when the circuit is broken at any
point?__________________________________________
______________________________________________.
• Set up a series circuit with the same power supply but with 2
lamps (i.e. remove one of the lamps from the above circuit).
Measure the current in the circuit. Compare this with the
value found with 3 lamps. ___________________________
______________________________________________.
30
The current in a series circuit is the _______________ at all
points.
As more lamps are added in series the current in the circuit
_________________.
Current _______ _______ split up in a series circuit.
Experiment 6(C):- Current in a Parallel Circuit
What you need: power supply, 3 lamps, an ammeter.
Set up the circuit as shown below. Check that all of the lamps are
lit.
A
B
C
D
2V
E
• Measure the current at positions A, B, C, D and E and complete
the table below
Position
Current / A
A
B
C
D
E
31
• What do you notice about the current at A and E?
_______________________________________________
• Add up the current at B, C and D. Current at B + C + D =
A
• What is the adding up the same as?____________________
In a parallel circuit, the current in the main circuit is ___________
to the ___________ of all the currents in the parallel branches.
Current _____________ _______ in a parallel circuit. There is no
loss of current in the circuit.
Ip = I1 + I2 + I3
For a parallel circuit
Is
−
I1
I2
I3
2V
+
L1
L2
L3
• Set up the circuit shown at the top of the page and measure
the current at position A.
• Leave the ammeter in position A.
• Unscrew the lamps one at a time and note the reading on the
ammeter each time.
In a parallel circuit, as more lamps are added the current in the main
circuit _______________.
32
Voltage or potential difference (p.d.)
Series circuit: the components are arranged in line – connected
end-to-end.
Parallel circuit: the components are connected across each other –
current has more than one path through that part of the circuit.
Experiment 7: Energy in a circuit
What you need: 3 batteries, lamp, leads.
• Look at the battery. What is the value of the voltage marked
on the battery?
• Set up each circuit, in turn, as shown above.
• Complete the table.
Number of batteries Voltage of batteries Brightness of lamp
1
2
3
33
As more batteries are added in series, the voltage i___________
and the lamp gets b_______________. Since the lamp gets
b_________________ it must be gaining more e_________ from
the e_______________ passing through it.
Increasing the voltage means that more e_________ is given to
each c_________ of charge that passes through the battery. This
electrical energy is changed into ________ and ________as the
charge passes through the lamp.
The voltage of a supply is a measure of the energy given to each
coulomb of charge as it passes through the supply.
34
Measuring potential difference or voltage
Potential difference or voltage is measured in ____(V) using a
________.
Circuit symbol:
V
Your teacher will demonstrate the following steps explaining how
to connect a voltmeter in a circuit.
• Set up the circuit.
• Identify the component or two points where the potential
difference is to be measured.
• Connect the voltmeter in parallel with the component or
between the two points.
• Do not make a gap in the circuit.
• Make sure that the positive terminal (+) marked on the
voltmeter is connected towards the positive terminal of the
power supply.
• If you obtain a negative reading on the voltmeter, reverse the
connections on the voltmeter.
+
−
−
+
A
−
+
B
A
B
+
35
V
Experiment 8(a): Potential difference (p.d.) in a Series Circuit
What you need: power supply, 2 lamps, voltmeter.
Set up the circuit as shown below.
A
−
4V
B
+
C
Measure the p.d. between points AB, BC, AC and the supply voltage.
Complete the table below.
Position
p.d. / V
AB
VAB =
BC
VBC =
AC
VAC =
Supply
VS =
• VAB + VBC =
• VS =
Potential differences in a series circuit _______ ____ to the supply
voltage.
VS =
Potential difference _______ _____ in a series circuit.
36
Experiment 8(b): Potential difference (p.d.) in a Parallel Circuit
What you need: power supply, 3 lamps, voltmeter, leads.
Set up the circuit as shown below.
+
2V
−
A
B
C
D
E
F
Measure the p.d. between points AB, CD, EF and the supply voltage.
Complete the table below
Position
p.d. / V
AB
VAB =
CD
VCD =
EF
VEF =
Supply
VS =
Potential differences across components connected in parallel are
always the s________.
VS =
In a parallel circuit the starting point and the finishing point for
each b________ is the s_____. When you measure the p.d. across
each b_________, you are measuring the _____ between the
s_______ two points – the _______ and the __________ of the
parallel circuit. Hence the p.d. across components connected in
p___________ is the s_______ since it is the same p.d. you are
measuring.
37
Experiment 9(a): Resistance
Circuit symbol for a resistor:
What you need: power supply, small resistance, large resistance,
ammeter, leads.
+
3V
+
−
3V
−
small resistance
large resistance
Circuit 1
Circuit 2
• Set up Circuit 1 as shown and measure the current.
• Set up Circuit 2 as shown and measure the current.
• Complete the table.
Circuit
Current / A
1
2
Resistance is a measure of the opposition of a circuit
component to current. The larger the resistance, the
s__________ the current.
As the electrons move through the component they collide with the
other particles (the atoms) that make up the component. This slows
the electrons down. Less charge is transferred in one second so
there is l______ current. This effect is called electrical resistance.
Resistance is due to collisions between electrons and particles in
a component.
38
Experiment 9(b): Measuring resistance
Resistance can be measured using an O___________.
Circuit symbol:
Ω
Resistance is measured in ____________ (Ω).
When measuring resistance with an o_____________ there should
be no current in the component.
The ohmmeter is connected across the component as shown.
Ω
The scale on the ohmmeter is altered until a reading is displayed on
the screen. This is the resistance of the component.
• Use the ohmmeter to find the resistance of the two resistors
used in Circuits 1 and 2 above. Complete the table.
Resistance Resistance /
Small
Large
39
Ω
Tutorial 2
1. Two identical 3·5 V bulbs are connected to a supply as shown.
What is the voltage of the supply?
3.5 V
3.5 V
2. Four identical resistors are connected across a 12 V supply as
shown in the diagram. What is the voltage across each of the
resistors?
12 V
A
B
C
40
D
3. A simple circuit with a bulb and resistor in series is shown
below.
36 V
R
12 V, 36 W
(a)
If the bulb is operating at its
correct voltage and power rating
what is the voltage across the
resistor R?
(b)
The current in the bulb is 3 A.
What current flows in the
resistor?
4. Two resistors are connected in parallel to a 12 V battery
12 V
0·4 A
R1
0·6A
R2
(a)
What is the voltage across R1? __________________
(b)
What is the voltage across R2?___________________
(c)
What size of current is drawn from the battery?_____
41
5. An electric fire has three elements (bars) which can be switched
on and off separately. The elements are connected in parallel to
the mains supply. Each element draws a current of 0·4 A when
switched on.
(a) What is the voltage across the
230 V
bottom element? ________________
(b) What is the total current flowing
from the supply when two of the
elements are switched on?__________
(c) What is the maximum current
drawn from the mains by the fire?____
6. The headlamps and side lights in a car are connected in
parallel. The diagram below shows how they are connected.
The side lights (L1 & L2) may be switched on by themselves
using switch S1. The headlights (H1 & H2) are switched on
by switch S2 and only come on if the sidelights are already
on.
S2
S1
12 V
L1
L2
H1
42
H2
(a)
What is the voltage across the sidelight L1?
________________________________
(b)
What is the voltage across the headlight H2?
________________________________
(c)
Each sidelight draws a current of 2 A from the car
battery. What is the total current drawn from the
battery when S1 only is closed?
______________________________________
(d)
Each headlight draws a current of 6 A from the car
battery. What is the total current drawn from the
battery when S1 and S2 are closed?
_______________________________________
43
Experiment 10: Potential difference, current and resistance
What you need: power supply, ohmmeter, 5 different resistors
(A, B, C, D and E), ammeter, voltmeter and leads.
+
4V
−
Ω
A
V
Circuit 1
Circuit 2
• Set up circuit 1 as shown above and measure the resistance (R)
of A, B, C, D and E.
• Record your answers in the table below.
• Set up circuit 2 as shown above.
• Use resistor A as the first resistor.
• Measure the current (I) in and the potential difference (V)
across resistor A.
• Record the value of the current and the corresponding
potential difference in the table below.
• Repeat this for resistors B, C, D and E.
• For each resistor calculate the value of V divided by I (V/I).
• Compare the value of V/I for each resistor with the resistance
of the resistor.
Resistor
R/Ω
V/V
A
B
C
D
E
44
I/A
V
I
The value for R and V are the s_________.
I
R=
I=
V=
V
The equation V =
is known as Ohm’s Law
I
R
Ohm’s Law
p.d. across a component = current in component x resistance of component
voltage across a component = current in component x resistance of component
V = I x R
V = voltage (or p.d.) across component measured in volts (V)
I = current in component measured in amperes (A)
R = resistance of component measured in ohms (Ω)
Using the “magic” triangle:
V = I x R
I = V/R
R = V/I
Example 1: The current in a 20 Ω resistor is 1.5 A. What is
the p.d. across the resistor?
V=?
I = 1.5 A
R = 20 Ω
V=IxR
V = 1.5 x 20
V = 30 V
45
Example 2: The voltage across a lamp is 12 V. The current in the
lamp is 4 A. Calculate the resistance of the lamp.
Example 3: The resistance of an electrical component is 22 Ω. The
p.d. across the component is 12 V. Calculate the current
through the component.
Example 4: If a 12V supply produces a current of 15 mA through
a resistor, calculate the resistance.
Example 5: What voltage is required to produce a 750 µA current
through a 330 kΩ resistor.
46
Experiment 11: Resistance Investigations
What you need: power supply, resistor, ray-box lamp,
ammeter, voltmeter, leads and an investigation booklet.
What to do:
Experiment A:
• Plan and carry out an experiment to find out what happens to
the resistance of a resistor when the p.d. across the resistor
changes from 0 to 12 V. Your plan should include an accurately
drawn circuit diagram.
• Take your readings quickly so that the resistor does not get
too hot!
• Calculate the resistance of the resistor at the following
voltages: 2V, 4 V, 6 V, 8 V, 10 V and 12 V
• Table for resistor readings
V /V
2
4
6
8
10
12
I / A
R / Ω
• Plot a graph of p.d. across the resistor against current in the
resistor
• Explain your results and make some valid conclusions based on
them
• Evaluate your procedure highlighting any possible
improvements
47
Experiment B:
• Plan and carry out an experiment to find out what happens to
the resistance of a lamp when the brightness of the lamp
changes (p.d. across the lamp changes from 0 to 12 V).
• Calculate the resistance of the lamp at the following voltages:
2V, 4 V, 6 V, 8 V, 10 V and 12 V
• Table for lamp readings
V /V
2
4
6
8
10
12
I / A
R / Ω
• Plot a graph of p.d. across the lamp against current in the
resistor
• Explain your results and make some valid conclusions based on
them
• Evaluate your procedure highlighting any possible
improvements
Summary of Results:
The resistance of a resistor remains constant provided the t__________ of
the resistor does not change.
The wire inside a lamp is called the filament. As the p.d. across the lamp
i__________, there is more e________ in the filament of the lamp – the
filament gets h___________. The brighter the filament gets the higher the
_____________of the filament. As the temperature of the filament increases
the resistance of the filament _____________.
If the temperature of a resistor _____________, the resistance of the
resistor ______________.
48
Experiment 12(a): Resistance and length of wire
What you need: power supply, ammeter, leads, 1 m of test
wire.
• Set up the circuit as shown below.
+
4V
−
A
X
• Place the moveable contact, X, so that 20 cm of the test wire
is in the circuit
• Record the current in the circuit in the table below
• Repeat for 40 cm, 60 cm, 80 cm and 100 cm of test wire.
Length of test wire / cm Current in circuit / A
20
40
60
80
100
As the length of wire increases, the current in the wire _________
and so the resistance of the wire has __________.
length of wire ↑ – resistance – current
In the above experiment, the length of the wire was changed (this is
the dependent variable), while the current in the wire ( the
___________ variable) was measured. The ____________of the
wire was not changed in order to keep the experiment fair.
49
Experiment 12(b): Resistance and thickness of wire
What you need: power supply, ammeter, 3 wires of equal
length but different thickness.
• Set up the circuit as shown below
+
4V
−
A
X
Y
• Place the thickest wire between the points X and Y
• Record the current in the circuit in the table below
• Repeat for the other two thicknesses of wire
Thickness of wire Current in circuit / A
Thick
Medium
Thin
As the wire gets thicker, the current in the wire
____________________ and so the resistance of the wire
has ____________________.
As thickness of wire ↑ – resistance
– current
In the above experiment, the thickness of the wire was changed
(this is the ________________ variable), while the current in the
wire (the ________________ variable) was measured. The ______
of the wire was not changed in order to keep the experiment fair.
50
Experiment 12(c): Variable Resistors
What you need: d.c. supply, lamp, variable resistor (rheostat), small
electric motor.
(a)
(b)
Circuit 1
Circuit 2
What to do:
1. Set up circuit 1 using the middle terminal and one end of the
variable resistor. Switch on and vary the brightness of the lamp.
2. Replace the lamp with the motor and alter its speed.
3. Set up circuit 2 - adjust the potentiometer to vary the brightness
of the lamp.
51
The variable resistor or rheostat works by ___________ or
___________ the length of wire in the circuit.
When the length of wire increases the resistance of the circuit
__________ and the current ___________ (lamp gets
_________).
The variable resistor (circuit 1) controls the size of the current in
the lamp.
The potentiometer (circuit 2) controls the size of the voltage that
is applied across the lamp.
Describe some practical applications of variable resistors:
___________________________________________________
___________________________________________________
___________________________________________________
___________________________________________________
___________________________________________________
___________________________________________________
52
Experiment 13(a): Measuring Resistances in Series
What you need: 3 fixed resistors R1, R2 and R3, ohmmeter and leads.
R1
Ω
•
•
•
•
•
Measure the resistance of R1 using the ohmmeter.
Measure the resistance of R2 using the ohmmeter.
Measure the resistance of R3 using the ohmmeter.
Record your results in the table below.
Connect R1, R2 and R3 in series as shown below.
A
R1
B
R2
R3
C
D
Ω
• Measure the total resistance RT of the three resistors in
series (connect ohmmeter between A and D)
Resistor
Resistance / Ω
R1
R2
R3
RT
• How does the total resistance RT compare with either R1, R2
and R3 ? ___________________________________
The total resistance of a number of resistors connected in series
( RT ) is equal to the _________ of the individual resistors.
RT =
.
Adding resistors in series __________________ the total resistance of the
circuit and so the circuit current will ____________________.
53
Experiment 13(b): Measuring Resistances in Parallel
What you need: 2 fixed resistors R1, and R2, ohmmeter.
R1
R2
Ω
Ω
• Measure the resistance of R1 using the ohmmeter.
• Measure the resistance of R2 using the ohmmeter.
• Record your results in the table below.
• Connect R1 and R2 in parallel as shown below.
R1
R1
A
D
Ω
• Measure the total resistance RT of the two resistors in parallel
(connect ohmmeter between A and D) and record your result in
the table.
Resistor
Resistance(Ω)
R1
R2
RT
54
1/ R
• How does the total resistance compare with either R1 or R2?
____________________________________________
1/RT=
.
Adding resistors in parallel d________________ the total
resistance of the circuit and so the circuit current will _________.
The total resistance of the circuit is _________ than the value of
the smallest resistance connected in parallel.
Example: Three resistors are connected as shown below. Calculate
the resistance between X and Y.
12 Ω
X
24 Ω
1 = 1+1+1 =
RXY R1 R2 R3
Y
1 + 1 + 1
12 24 20
1 = 0.083 + 0.042 + 0.050 = 0.175
RXY
20 Ω
RXY =
1
0.175
RXY = 5.7 Ω
55
.
Resistance in Series and in Parallel
Example 1: Three resistors are connected as shown below.
Calculate the resistance between X and Y.
X
10 Ω
15 Ω
8Ω
Y
RXY = R1 + R2 + R3
RXY = 10 + 8 + 15
RXY = 33 Ω
Example 2: Two resistors are connected as shown below. Calculate
the resistance between X and Y.
X
Y
1 = 1+1= 1 +1 = 2
RXY R1 R2 24 24 24
24 Ω
1 = 2
RXY 24
24 Ω
RXY = 24
1
2
RXY = 12Ω
Example 3: A resistor network is shown below. Calculate the
resistance between X and Y.
15 Ω
X
A
7Ω
Y
30 Ω
56
Series and parallel circuits – Summary
Series circuit
• There is only one path for current
• Current is the same at all points – but changes if the
resistance of the circuit changes
• Potential differences (voltages) add up to the supply voltage
• Adding resistors in series increases the resistance of the
circuit
• RT = R1 + R2 + R3
Parallel circuit
• There is more than one path for current
• The currents in the branches add up to the current from the
supply
• Potential differences (voltages) are the same
• Adding resistors in parallel decreases the resistance of the
circuit
• 1 = 1+1+1
RT R1 R2 R3
Prefixes to units
So far in this unit we have measured
• charge in coulombs (C)
• p.d. in volts (V)
• current in amperes (A)
• resistance in ohms ()
We sometimes have to measure physical quantities in smaller or
bigger values. These bigger or smaller values are represented by
prefixes.
57
You need to know the following prefixes:
• µ means micro or 10−6 (divide by 1,000,000)
• m means milli or 10−3 (divide by 1,000)
• k means kilo or 103 (multiply by 1,000)
• M means mega or 106 (multiply by 1,000,000)
e.g.
2.2 MΩ = 2.2 x 106 = 2.2 x 1 000 000 = 2,200,000 Ω
4µC = 4 x 10−6 =
4
= 0.000004 C
1 000 000
58
Tutorial 3
1. Look at the following circuits and calculate the current in
each case:
(a)
12 V
(b)
16v
48v
I
I
12 Ω
(a)
(c)
I
60 Ω
150 Ω
(b)
(c)
2. Look at the following circuits and calculate the unknown
resistance in each case:
(a)
12 V
24 V
(b)
48 V
60 µA
15 mA
R
(a)
(c)
330 µA
R
R
(b)
(c)
59
3. Calculate the resistance of a
lamp if the current through it is
8 mA when operated by a 12 V
supply.
4. A power drill is operated at
mains voltage and has a
resistance of 1·8 kΩ. Calculate
the current through the drill.
5. A cooker draws a maximum
current of 38·25 A and has a
resistance of 10 Ω. At what
voltage should it operate?
6. Hairdryers work from the
mains voltage and can have
currents of up to 25 mA
flowing through them.
Calculate the resistance of
the hairdryer.
60
7. Calculate the total resistance of the following circuit.
600 Ω
6kΩ
3·2 kΩ
8. The resistance of the following circuit is 9·8 kΩ. Calculate
the resistance of R.
850 Ω
R
6.8 kΩ
9. Calculate the equivalent resistance between X and Y in
each of the following networks, showing all the working
for each one:
(a)
(b)
4Ω
12 Ω
4Ω
12 Ω
61
(c)
16 Ω
16 Ω
16 Ω
(d)
6Ω
2Ω
12 Ω
10. A student designs the circuit shown to operate a 12 V, 3
A lamp from a 36 V supply.
(a)
What is the reading on the ammeter when the lamp is
operating at its correct power rating? _____________
(b)
The resistance of Rx is 2 Ω.
Calculate the voltage across Rx when
the lamp is operating correctly.
62
(c) Calculate the resistance of Ry
when the lamp is operating correctly.
(d) The student connects a second, identical lamp as shown in the
diagram below.
Explain why the resistance of Ry has to be adjusted for both lamps
to operate correctly.
___________________________________________________
___________________________________________________
___________________________________________________
11. A mains electric fire has two heating elements which can be
switched on and off separately. The heating elements can be
switched on to produce three different heat settings: LOW,
MEDIUM and HIGH. The fire also has an interior lamp which
can be switched on to give a log-burning effect.
The circuit diagram for the fire is shown below:
63
(a)
When switch S1 is closed,
the lamp operates at its
stated rating of 60W.
Calculate the current in the
lamp.
(b) Switch S1 is opened and switches S2 and S3 are closed.
(i)
Calculate the combined
resistance of both
heating elements.
(ii)
Calculate the total
power developed in the
heating elements
when S2 and S3 are
closed.
64
(iii) State and explain which switch or switches would have to be
closed to produce the LOW heat setting.
___________________________________________________
___________________________________________________
___________________________________________________
___________________________________________________
___________________________________________________
___________________________________________________
___________________________________________________
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Unit 2: Section 1 - Additional notes
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