Topic 1.3 – Circuit Concepts.
Learning Objectives:
At the end of this topic you will be able to;
 recognise standard symbols for components included within the
module;
 apply the current at a junction rule;
 apply the voltage divider rule;
 explain how voltage at a point can be indicated relative to a 0V
reference;
 appreciate that resistance is the opposition to current flow and that
is measured in ohms;
 understand the relationship between current, voltage and resistance
in qualitative terms;
 select and use R 
V
;
I
 recognise that analogue signals are continuously varying and digital
signals are two state;
 state the power is dissipated when current flows through resistance
and is measured in watts;
 understand the relationship between current, voltage and power in
qualitative terms;
 perform calculations involving P  V  I ;
 recognise and use the following multiple and sub-multiple indicators:
p, n, µ, m, k, and M.
1
GCSE Electronics.
Unit E1 : Discovering Electronics
Circuit symbols
Electronic circuits consist of components (parts) such as lamps, resistors and
transistors connected to an electrical supply, e.g. a battery. The connections
are wire or strips of a good electrical conductor such as copper. The
connections and components must make a complete path, i.e. a circuit.
Circuits are represented by diagrams in which each part is shown by a symbol.
Some examples that you should recognise are shown below are given below.
Using the circuit symbols above, draw a circuit diagram for a circuit
containing a battery, a resistor, two lamps, a switch and an ammeter.
2
Topic 1.3 – Circuit Concepts.
Electric Current
What is it
An atom consists of a tiny core or nucleus with a positive (+) electric charge,
surrounded by electrons which have an equal negative (-) charge. (see below)
Electrons (-)
Nucleus (+)
In a conductor, some electrons are loosely attached to their atoms. When the
conductor is part of a circuit connected to a battery, the battery forces
these electrons to move through the conductor from its negative (-) terminal
towards its positive (+) terminal. An electric current is said to be flowing
through the conductor when these electrons flow in one direction at a given
time.
The ampere and ammeters
Current is measured in units called amperes (shortened to amps or A). The
current flowing in a circuit can be measured with an ammeter. The current
through a large torch bulb is about 0.5A and through a car headlamp 3A to
4A.
3
GCSE Electronics.
Unit E1 : Discovering Electronics
Individual ammeters are hardly ever used for circuit measurements as it is
too expensive to have a large range of ammeters capable of reading different
currents. Today we use an instrument called a multimeter which is capable of
measuring lots of different currents and many other things besides all in one
package. The multimeter will become a very important instrument for you.
There are two main types of multimeter available. The first type is called an
analogue meter and is shown below.
One terminal is marked ‘+‘ (or coloured red) and this is the one the
conventional current must enter, that is, it must lead to the ‘+‘ terminal of
the battery. Otherwise the pointer on the ammeter is deflected in the wrong
direction and the ammeter may be permanently damaged.
The analogue meter has a moving needle which moves across multiple scales
and it is up to the user to interpret the correct reading. To the
inexperienced user this instrument is very hard to use and errors are
frequently made. Good quality analogue meters are very expensive (over
£100.00) although cheaper versions are available they are not always very
accurate.
4
Topic 1.3 – Circuit Concepts.
More common these days are the digital multimeter as shown below:
The digital meter is much easier to use than an analogue meter because it
gives a direct reading on its display of the quantity that it is measuring. The
digital meter also has a red terminal which should be connected to the
positive part of the circuit, however, unlike the analogue meter if a mistake is
made all that will happen is that the display will shown a ‘-’ sign in the display
to indicate that current is flowing the wrong way. To rectify the problem
simple reverse the connections in the circuit. No damage will be done to the
multimeter.
Throughout this course you should use a digital meter if at all possible during
some of your practical work. During computer modelling sessions you will use a
computerised version of the digital multimeter.
5
GCSE Electronics.
Unit E1 : Discovering Electronics
In either case the symbol used for an ammeter is shown below.
Note :
The symbol shown is for an ammeter because of the letter ‘A’ in
the circle. There is no separate symbol for a multimeter, because
as it’s name suggests the multimeter can be set up as a number of
different meters, one of which is an ammeter.
Two smaller units of current used in electronics are the milliampere
(mA) and the microampere (µA); (pronounced mu A).
1 A or 1000mA  1A
1000
1
1A  1 mA 
A or
1000
1000000
1000A  1mA or 1000000A  1A
1mA 
To be able to convert between these units accurately and reliably is very
important for calculations needed later. The following diagram will hopefully
help.
x1000
A
x1000
uA
mA
/1000
/1000
Examples :
1.
Convert the following currents into mA.
(1)
(2)
(3)
6
3A = 3 x 1000 = 3000 mA
1.5A = 1.5 x 1000 = 1500 mA
0.65A = 0.65 x 1000 = 650 mA
Topic 1.3 – Circuit Concepts.
2.
Convert the following currents into µA.
(1)
(2)
(3)
3.
2A = 2 x 1000 = 2000 mA = 2000 x 1000 = 2,000,000 µA
1.8mA = 1.8 x 1000 = 1800 µA
0.32A = 0.32 x 1000 = 320 mA = 320 x 1000 = 320,000 µA
Convert the following currents into A.
(1)
(2)
(3)
1,500,000 µA = 1,500,000 ÷ 1000 = 1500 mA = 1500 ÷ 1000 = 1.5 A
1.3mA = 1.3 ÷ 1000 = 0.0013 A
65,000 µA = 65000 ÷ 1000 = 65 mA = 65 ÷ 1000 = 0.065 A
There are other multipliers that we will come across in this course, which are
for very small quantities, these are ‘p’ for pico, and ‘n’ for nano. We will look
at these when we consider capacitors in Unit E2.
Measuring Current
To measure a current, the circuit has to be broken and the ammeter
connected in the gap.
To complete this part of the exercise you will need access to a computer
running circuit simulation software e.g. Crocodile Physics or Livewire.
7
GCSE Electronics.
Unit E1 : Discovering Electronics
(a)
Series circuit
Within your simulation software create the following circuit using the
circuit symbols shown.
In your circuit you will not get the labels alongside the circuit symbols these
are included so that you can answer the questions about the circuit.
When you have successfully constructed the circuit on the computer the
three ammeters will display the current flowing at each part of the circuit
and both lamps should be on.
Note : The readings on each ammeter should be positive. If you have a
negative value it means you have connected the ammeter incorrectly - check
the circuit carefully and correct before answering the questions.
Complete the following to show your results.
Ammeter 1 = ....... mA
Ammeter 2 = ....... mA
Ammeter 3 = ....... mA
Looking at your results what conclusion can you make about the current
flowing in a series circuit ?
........................................................................................................................................
........................................................................................................................................
Save your circuit as “Basic-Theory-Circuit1”.
8
Topic 1.3 – Circuit Concepts.
(b)
Parallel circuit
Within the simulator create the following circuit using the circuit
symbols shown.
Note: In your circuit you will not get the labels alongside the circuit symbols
these are included so that you can answer the questions about the
circuit. Please remember to change the battery voltage to 6V
When you have successfully constructed the circuit, the four ammeters will
display the current flowing at each part of the circuit and both lamps should
be on. Note : The readings on each ammeter should be positive. If you have a
negative value it means you have connected the ammeter incorrectly - check
the circuit carefully and correct before answering the questions.
Complete the following to show your results.
Ammeter 1 = ........ mA
Ammeter 2 = ........ mA
Ammeter 3 = ........ mA
Ammeter 4 = ........ mA
Looking at your results what conclusion can you make about the current
flowing in a parallel circuit?
........................................................................................................................................
.......................................................................................................................................
Save your circuit as “Basic-Theory-Circuit2”.
9
GCSE Electronics.
Unit E1 : Discovering Electronics
(c)
Circuit drawn with voltage rails
If a supply has a voltage of, say, 9V, you will often find on circuit diagrams
that the negative of the supply is marked as 0V and the positive as 9V, as
shown below.
l
Notice the way the current I flows in the two circuits
You will see later on that using voltage rails can help to make the drawing of
electronic circuits easier.
(d)
Series /Parallel circuit
Consider the following circuit which contains 2 different signal lamps and a
filament lamp connected to a 9V power supply. You will notice that a filament
lamp has a different symbol to the signal lamp.
Complete the following table for this circuit using the values of I1 and I2 given.
10
Topic 1.3 – Circuit Concepts.
Remember that the sum of currents entering a junction is always equal to the
sum of currents leaving a junction.
For this circuit this means that:
I1  I 2  I 3
I2  I3  I 4
I 4  I5
Current
Value
I1
100mA
I2
30mA
I3
I4
I5
Ask your teacher to check your answers
Conductors, insulators and semiconductors
The best conductors are the metals silver, copper and gold because they
contain electrons that are free to move.
In insulators such as polythene and PVC (polyvinyl chloride) all electrons are
firmly bound to their atoms and electron flow, i.e. current production, is
difficult.
Semiconductors like silicon and germanium conduct to a certain extent.
11
GCSE Electronics.
Unit E1 : Discovering Electronics
Summary 
1.
Electronic circuits consist of components e.g. lamps, batteries
connected by wires.
2.
Electric current is the flow of electrons through a material.
3.
Current flows from the positive terminal to the negative terminal of the
battery.
4.
Current is measured in A, mA or µA.
5.
1A = 1000 mA = 1,000,000 µA
6.
Current is not used up in an electrical circuit. Whatever current leaves
the battery must return to the battery.
7.
In a series circuit the current is the same at all points in the circuit.
8.
In a parallel circuit the current splits at the junction of three or more
wires. The sum of currents entering a junction is always equal to the sum
of currents leaving a junction.
12
Topic 1.3 – Circuit Concepts.
Homework Questions 1:
1.
In the circuit below, if Ammeter 1 reads 0.2A what are the readings on
Ammeter 2 and Ammeter 3.
Circle the correct answers;
2.
Ammeter 2
0A 0.1A 0.2A
0.3A
0.4A
Ammeter 3
0A 0.1A 0.2A
0.3A
0.4A
Study the 3 circuits below carefully.
If a lamp breaks, no current flows in that part of the circuit.
a.
if one lamp fails, in which of the circuits A, B or C will the total
number of lamps going out be one ? Answer =
b.
if one lamp fails, in which of the circuits A, B or C will the total
number of lamps going out be two ? Answer =
c.
if one lamp fails, in which of the circuits A, B or C will the total
number of lamps going out be four ? Answer =
[3]
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GCSE Electronics.
Unit E1 : Discovering Electronics
3.
In the diagram below, if Ammeter 2 reads 0.3A and Ammeter 4 reads
0.5A, what does Ammeter 1 and Ammeter 3 read ?
Circle the correct answers;
4a.
Ammeter 1
0.1A
0.2A
0.3A
0.4A
0.5 A
Ammeter 3
0.1A
0.2A
0.3A
0.4A
0.5 A
[2]
Convert the following currents into mA:
(i)
1A
=
(ii)
0.5 A =
(iii) 0.02 A =
(iv) 0.0045 A =
4b.
Convert the following currents into A:
(i)
1500 mA =
(ii)
300 mA =
(iii) 60 mA =
14
[4]
[3]
Topic 1.3 – Circuit Concepts.
4c.
Convert the following currents into µA:
(i)
2 mA =
(ii)
0.4 A =
(iii) 0.005 mA =
[3]
5.
Complete the following table for this circuit
Current
Value
I1
250mA
I2
100mA
I3
I4
I5
[3]
15
GCSE Electronics.
Unit E1 : Discovering Electronics
Voltage
What is it?
Voltage (symbol V) causes current to flow in a circuit by applying an electrical
pressure across it. It is produced by a cell, a battery or a power supply.
Voltage is measured in volts (shortened to V). Just as we had smaller units
for current in the last section we can also have smaller units of voltage. The
millivolt (mV) and microvolt (µV) are defined as
1
V
1000
1
1
1V 
mV 
V
1000
1000000
1mV 
Note :
There will be a current in a conductor only when there is a
voltage across it.
The voltage of a carbon-zinc or dry cell, shown below is 1.5 V.
Two cells connected in series, that is the ‘+’ terminal of one to the ‘-’
terminal of the other, have a voltage of 2 x 1.5 V = 3 V.
In a 9 V battery, shown opposite, six 1.5V cells are
internally connected in series.
16
Topic 1.3 – Circuit Concepts.
Voltmeters
A voltmeter is used to measure voltage in a circuit. Separate voltmeters like
those shown below are rarely used today because of the need to have a range
of meters capable of measuring different voltages.
Instead the digital multimeter is the normal instrument used for a voltmeter,
in exactly the same way as it is used for an ammeter, the only difference may
be is which sockets you use on the multimeter and how it is connected into
the circuit. Just like an ammeter, its ‘+‘ terminal (often coloured red) must
lead to the ‘+’ terminal of the voltage supply being measured. Otherwise the
voltmeter will show a negative voltage. Note : Even though a negative voltage
is displayed no damage is being done to the meter. The circuit symbol for a
voltmeter is as follows:
Voltage is used up in a circuit
If there is current in any part of a circuit, there must be a voltage drop
across that part. The drop is measured by connecting a voltmeter across that
part, i.e. in parallel with it (Note : This is the opposite to an ammeter, which
is connected in series to measure current).
To complete this part of the exercise you will need access to a computer
running a circuit simulation package. e.g Crocodile Physics or Livewire.
17
GCSE Electronics.
Unit E1 : Discovering Electronics
(a)
Series circuit
Within the simulation package
create the circuit opposite.
Note:
In your circuit you will not get the labels alongside the circuit
symbols these are included so that you can answer the questions
about the circuit. Remember to set the voltage of the battery
to 9V.
Record the reading on all three voltmeters in the spaces below :
Voltmeter 1 = ......... V,
Voltmeter 2 = ......... V,
Voltmeter 3 = .........
What conclusion can you make about your results.
........................................................................................................................................
........................................................................................................................................
Save your circuit as “Basic-Theory-Circuit3”.
18
Topic 1.3 – Circuit Concepts.
(b)
Parallel circuit
Set up the following circuit in your simulator.
Record the reading on the two voltmeters in the spaces below :
Voltmeter 1 = ......... V;
Voltmeter 2 = ......... V
What conclusion can you make about your results.
........................................................................................................................................
........................................................................................................................................
........................................................................................................................................
Save your circuit as “Basic-Theory-Circuit4”.
(c)
Series/Parallel circuit
In the circuit opposite the 2
signal lamps are in parallel with
each other, so the voltage is
the same across each of them.
The filament lamp is in series
with this parallel combination
so the voltage across this plus
the voltage across the signal
lamps equals 9V.
So V1 = 3V, and V2 = 9V - 3V = 6V
Summary 
1.
Voltage is the force which drives current around a circuit.
19
GCSE Electronics.
Unit E1 : Discovering Electronics
2.
Voltage is measured in volts, V, millivolts, mV or microvolts, µV.
3.
1V = 1000 mV, 1mV = 1000µV.
4.
Voltage is used up in any electrical circuit.
5.
In a series circuit the sum of voltages around the circuit is equal to the
voltage of the battery.
6.
In a parallel circuit the voltage is the same across all components in
parallel.
7.
Cells can be connected together in series to increase the voltage
available. However they must be connected positive to negative. If they
are connected positive to positive then they cancel each other out.
Homework Questions 2:
1.
20
What are the voltages of the batteries made up of 1.5V cells connected
as shown in the following circuits
Topic 1.3 – Circuit Concepts.
Circle the correct answers;
2.
Battery (a)
1.5V
3V
4.5V
6V
7.5V
Battery (b)
1.5V
3V
4.5V
6V
7.5V
[2]
Three voltmeters V, V1, V2 are connected as shown below.
(a) If V reads 9V and V1 reads
6V, what does V2 read ?
V2 =
[1]
(b) The table below gives the voltmeter readings that were obtained with
the circuit when 2 different batteries were used.
Complete the table by calculating the 2 missing voltages.
Reading in Volts
V
V1
V2
12
12
3.
6
4
In the circuit below what is the voltage drop across
(a) AB, (b) CD ?
[2]
VAB =
21
GCSE Electronics.
Unit E1 : Discovering Electronics
VCD =
4.
[2]
What are the values of VS and V1 in the following circuit?
VS =
V1 =
[2]
5a.
Change the following to mV.
(i) 1 V =
5b.
(ii) 0.7 V =
[3]
Change the following to V
(i) 1600 mV =
(ii) 400 mV =
Resistance
What is it?
22
(iii) 0.02 V =
(iii) 50 mV=
[3]
Topic 1.3 – Circuit Concepts.
Electrons move more easily through some conductors than others. Opposition
to current is called resistance. The current caused by a certain voltage is
greater in a good conductor than in a poor one. We use this fact to measure
resistance.
If the current through a conductor is I when the voltage across it is V,
its resistance R is given by the equation
R
V
I
This formula (known as Ohm’s Law) will be provided in your examinations.
Circuit calculations
Sometimes ‘R’ is known and we have to calculate ‘V’ or ‘I’. The above
equation for R can be rearranged so that
(i)
V can be found when R and I are known using the equation
V  IR
(ii)
I can be found when R and V are known using the equation
I
V
R
The triangle opposite can be used to work out
the formula required to solve problems of this
type. Simply cover the term you want to find
and what is left is the formula to use.
23
GCSE Electronics.
Unit E1 : Discovering Electronics
Worked examples
1.
Find the voltage across a wire of resistance 10Ω carrying a current of
0.5A?
First write down what you know from the question.
R = 10Ω, I = 0.5A, V = ?
Then write down the equation: R 
V
, rearrange to make V the subject –
I
V  IR
Substitute the known values and solve:
2.
V  IR
 0.5  10
 5V
Calculate the current through a wire of resistance 3Ω when there is a
voltage of 9V across it.
First write down what you know from the question.
R = 3Ω, I = ?, V = 9V
Then write down the equation: R 
I
V
, rearrange to make I the subject –
I
V
R
Substitute the known values and solve:
I
24
V 9
  3A
R 3
Topic 1.3 – Circuit Concepts.
Two important points about units
1.
Two larger units of resistance are the kilohm (kΩ) and the megohm
(MΩ).
1 kΩ = 1000Ω;
2.
1MΩ = 1,000,000Ω
In electronics ‘I’ is often in mA and R in kΩ. Using these units, V is still
in volts. For example, if
(a)
I = 2 mA and R = 10 kΩ, then
V IR
 (2mA)  (10k)
2
(
)  (10  1000)
1000
 2  10
 20V
(b)
I = 2 mA and V = 4Ω, then
R
V
I



4V
4
4 





2
2mA 
0.002 
 1000

 2k
(d)
R = 2kΩ and V = 6V, then
V
R
6V 
6
6




 0.003 A

2k  2  1000 2000

 3mA
I
25
GCSE Electronics.
Unit E1 : Discovering Electronics
Resistors
Resistors are conductors that are specially made to have resistance. They
limit the current to a desired value when connected in series in a circuit.
Fixed resistors have resistance values fixed at the time of manufacture.
The symbol for a fixed value resistor is shown below:
We will be considering resistors in more detail in the next chapter.
Using a resistor is to limit the current flowing in a circuit
Set up the following circuit in your simulator.
Record the reading on the ammeter in the space below :
Ammeter reading = ......... mA
Change R1 to 200 and record the reading on the ammeter;
Ammeter reading = ......... mA
Use your results to complete the following:
The larger the resistance in the circuit the …………………… is the brightness of
the lamp and the…………………… is the current flowing.
26
Topic 1.3 – Circuit Concepts.
Now set up this circuit in your simulator.
Record the reading on the ammeters in the space
below :
Reading on ammeter connected to 200 resistor=
......... mA
Reading on ammeter connected to 100 resister=
......... mA
Use your results to complete the following:
In a parallel circuit the .............................. current flows through the branch
with the ........................... resistance.
Worked example
1.
The diagram shows part of a circuit.
(a) What is the value of I5
I5 = 10 mA [the same as the current entering on the left]
(b)
Which is the bigger resistor, R2 or R3?
R2 [smallest current flows through largest resistor]
27
GCSE Electronics.
Unit E1 : Discovering Electronics
(c)
Calculate current I4.
Answer: I4 = 1mA
(d)
[ 10mA - 8mA – 1mA = 1mA]
What can you say about the sizes of resistors R3 and R4?
R3 and R4 are equal because they are in parallel and equal
currents flow through them
(e)
Calculate the voltage across resistor R1.
V = I x R = 10mA x 1k = 10V
2.
Look at the diagram and write down the values of the following:
(a)
I1 = 10mA [12mA – 2mA]
(b)
I2 = 12mA [10mA + 2mA]
(c)
V1 = 7V [9V – 2V]
(d)
Calculate the value of R1
R
28
V
2V

 1k
I 2mA
Topic 1.3 – Circuit Concepts.
Summary 
1. Resistance is the opposition to electric current.
2. Resistance is measured in ohms, symbol, .
V
I
4. 1Ω is a very small unit of resistance, it is more usual to quote
3. Resistance can be calculated using the formula R 
resistance in kΩ, or MΩ.
5. 1kΩ = 1000Ω, 1MΩ = 1,000,000Ω
6. Resistors are conductors made especially to have resistance.
7. Fixed resistors have a value of resistance fixed at the time of
manufacture.
8. Resistors can be used to limit the current flowing in a circuit
29
GCSE Electronics.
Unit E1 : Discovering Electronics
Homework Questions 3:
1.
Study the circuit diagram below.
(a)
Calculate the reading on the ammeter. (You can assume that the
ammeter has no resistance.)
.............................................................................................................................
(b)
.............................................................................................................................
[2]
What is the voltage across the lamp of resistance 6.
Voltage =
2.
(a)
[1]
What is the resistance of a resistor when a voltage of 6V across it
causes a current of 1.5A ?
.............................................................................................................................
(b)
.............................................................................................................................
[2]
Calculate the voltage across a 10 resistor carrying a current of
2A.
.............................................................................................................................
.............................................................................................................................
[2]
30
Topic 1.3 – Circuit Concepts.
3.
Look at the circuit shown below.
V
I
Calculate
(a)
R
V if I = 5 mA and R = 2 kΩ
.............................................................................................................................
(b)
.............................................................................................................................
[2]
R if V = 12V and R = 3 mA
.............................................................................................................................
(c)
.............................................................................................................................
[2]
I if V = 10V and R = 5 kΩ
.............................................................................................................................
.............................................................................................................................
[2]
31
GCSE Electronics.
Unit E1 : Discovering Electronics
4.
Look at the following diagram.
(a) Write down the values of
the following:
I1 =
mA
I2 =
mA
V1 =
V
V2 =
V
I3 =
mA
[5]
(b) Calculate the value of resistor R
.......................................................................................................................................
.......................................................................................................................................
[2]
32
Topic 1.3 – Circuit Concepts.
Voltage dividers
Consider the following system diagram and its corresponding circuit diagram
of a temperature sensing Unit
Temperature Sensing Unit
The circuit diagram contains a temperature dependent resistor and a variable
resistor connected across a battery. This circuit arrangement is called a
voltage divider circuit.
As the temperature changes so will the value of VOUT. In electronics we are
often interested in predicting the value of VOUT in voltage divider circuits.
If the resistance of the variable resistor is set to 100and the resistance
of the temperature dependent resistor at a certain temperature is 200 we
can work out the value of VOUT as follows:
Total resistance of circuit = 200 + 100300

Voltage across these resistors = 9V
Using formula I 
V
9
we get I 
 0.03 A
R
300
We can now find VOUT by using formula V  I  R
We now get VOUT  0.03  200  6V
33
GCSE Electronics.
Unit E1 : Discovering Electronics
As you can see to find VOUT we did an addition followed by a division followed
by a multiplication.
You will need to work out the value of VOUT for numerous voltage divider
circuits many times over the next 2 years so luckily there is a formula that
can be used to calculate VOUT . This formula is called the voltage divider rule
Voltage Divider Rule
Two resistors connected in series with a battery or power pack each have a
voltage across them. They may be used to divide the voltage of the supply.
This is illustrated below.
I
R1
V1
R2
V2
V
V2 
V  R2
( R1  R2 )
Example: Calculate the reading on the voltmeter in the following circuit.
9  24
(3  24)
9  24
V2 
 8V
27
V2 
3
9V
24
34
?V
Note: the 2 resistor values must be in the same
units, that is both values must either be in Ω, kΩ,
or MΩ.
Topic 1.3 – Circuit Concepts.
Worked Examples
Example 1: Calculate VOUT and V1 in the following circuit
V  R2
V

Using 2 ( R  R )
1
2
VOUT 
15  200
3000

 6V
(300  200) 500
V1 = 15 – 6 = 9V
Example 2: Calculate VOUT and V1 in the following circuit
V  R2
Using V2  ( R  R )
1
2
VOUT 
12  1 12

 6V
(1  1) 2
V1 = 12 – 6 = 6V
Example 3: Calculate VOUT and V1 in the following circuit
1.2kΩ = 1200Ω
V  R2
V

Using 2 ( R  R )
1
2
VOUT 
5  1200
6000

 4V
(300  1200) 1500
V1 = 5 – 4 = 1V
35
GCSE Electronics.
Unit E1 : Discovering Electronics
Note:
In examples 1 and 3 above you should notice that the largest voltage
appears across the largest resistor in each case. Always make this
check to make sure your answer is sensible in case you mixed up the 2
resistor values when substituting into the formula
In example 2 the two resistor values were the same so the voltage
values obtained were the same. You can use this result to write down the
answer when a voltage divider contains equal value resistors. Half the
supply voltage appears across each of the two resistors.
So for example 2 we could simply have written
VOUT  V1 
12
 6V
2
We will see more of these voltage divider circuits when we look at the
construction of sensor circuits.
36
Topic 1.3 – Circuit Concepts.
Exercise: Calculate VOUT and V1 in each of the following circuits. Show all
your workings out.
1.
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
2.
……………………………………………………………………………………………
……………………………………………………………………………………………
……………………………………………………………………………………………
……………………………………………………………………………………………
3.
……………………………………………………………………………………………
……………………………………………………………………………………………
……………………………………………………………………………………………
……………………………………………………………………………………………
Answers : 1. VOUT = 4 V, V1 = 2V;
2. VOUT = 5V, V1 = 4V;
3. VOUT = 3.6V, V1 = 14.4V
Try setting these circuits up on your simulator to confirm the answers.
37
GCSE Electronics.
Unit E1 : Discovering Electronics
Voltage at a Point
In electronic circuits it is often convenient to measure the voltage at a
particular point in the circuit rather than measure the voltage across a
component. The voltage at all points in a circuit can be measured with respect
to a single reference point. The 0V rail is normally used as the reference
point
Look at the circuit below which is from a circuit simulator:
There are 5 equal resistors across a 5V power supply so there is a voltage
drop of 1V across each resistor as shown on the voltmeters.
The cursor was held on the wire just above resistor R3 and the simulator
displayed the voltage at that point which is 3V. This gives the same answer
as adding up the voltage dropped across resistors R5, R4 and R3.
38
Topic 1.3 – Circuit Concepts.
Electrical Power
Power is a measure of how much energy is used per second in an electrical
appliance. When current flows through a resistance for example some heat is
developed as the current passes through the resistor some heat is produced,
and represents some wasted energy. We usually try to limit the amount of
power lost (dissipated) in circuit components because this is a waste of
energy, however it is necessary in some components like lamps / bulbs
because it is the heat generated in the filament of the lamp which causes the
light to be given off. Calculation of the power dissipated in any component is
relatively straight forward to do, by applying the following formula.
P  I V
Power(Watts)  Current ( Amps)  Voltage(Volts)
The current must be the current actually flowing through the component, and
the voltage must be the voltage across the component, which will give the
Power dissipated in the component in Watts.
Examples:
1.
Calculate the power dissipated in a 20Ω resistor, if the current flowing
through the resistor is 0.2A and the voltage across it is 5V.
P  I V
 0.2  5
 1W
2.
Calculate the power dissipated in a light bulb, if the current flowing
through the lamp is 60mA and the voltage across it is 6V.
P  I V
60

6
1000
 0.36W  360mW
39
GCSE Electronics.
Unit E1 : Discovering Electronics
3.
Calculate the current flowing through a 48W lamp when connected to a
12V power supply.
P  I V
P
V
48

 4A
12
I
Now a couple for you to do!
1.
Calculate the power dissipated in a kettle, if the current flowing
through the kettle is 9A and the voltage across it is 230V.
......................................................................................................................................
......................................................................................................................................
2.
Calculate the power dissipated in a 330Ω resistor, if the current
flowing through the resistor is 2.5mA and the voltage across it is 6V.
......................................................................................................................................
......................................................................................................................................
3.
Calculate the current flowing through a 100W lamp when connected to a
20V power supply.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
40
Topic 1.3 – Circuit Concepts.
Analogue and Digital Signals
The last thing to be introduced in this topic is the difference between an
analogue and digital signal. We have already seen in Topic 1.2 that some input
sensors are able to produce a wide range of voltage at their output, and these
have been called analogue sensors. Other sensors like the switch unit,
produced just two output voltages, and the transfer between them occurred
rapidly. These were called digital sensors. We need a better definition of
both of these signals so that we are completely clear about what they mean.
An analogue signal.
Voltage
Vmax
Vmin
An analogue signal, as shown above can take any value between the minimum
and the maximum voltage of the power supply. Changes may occur slowly, or
more rapidly. There are an infinite number of possible outcomes.
A digital signal.
Voltage
Vmax
Vmin
A digital signal, as shown above can only take one of two values. Either at the
minimum or the maximum voltage of the power supply. Changes occur
instantly. There are two possible outcomes.
41
GCSE Electronics.
Unit E1 : Discovering Electronics
Module E1 - Basic Theory
Solutions to Homework Questions
Homework Questions 1
1.
Ammeter 2 = 0.2A
Ammeter 3 = 0.2A
{this is because it is a series circuit and the current in a series circuit is
the same at all points in the circuit}
[2]
2.
a)
b)
c)
if one lamp fails, circuit B will be the only circuit in which the total
number of lamps going out will be one, this is because circuit B has
all four lamps in parallel.
if one lamp fails, circuit C will be the only circuit in which the total
number of lamps going out will be two, this is because circuit C has
two lamps in each parallel branch. Within each branch there are
two lamps in series and so when one lamp fails the other lamp in
the same branch will also go out.
if one lamp fails, circuit A will be the only circuit in which the total
number of lamps going out will be four, this is because circuit A
has all four lamps in series.
[3]
3.
Ammeter 1 = 0.5A
4a.
(i)
(ii)
(iii)
(iv)
4b.
42
Ammeter 3 = 0.2A
1 A = 1 x 1000 = 1000 mA
0.5 A = 0.5 x 1000 = 500 mA
0.02 A = 0.02 x 1000 = 20 mA
0.0045 A = 0.0045 x 1000 = 4.5 mA
(i)
1500 mA = 1500 ÷ 1000 = 1.5A
(ii) 300 mA = 300 ÷ 1000 = 0.3A
(iii) 60 mA = 60 ÷ 1000 = 0.06A
[2]
[4]
[3]
Topic 1.3 – Circuit Concepts.
4c.
(i)
2 mA = 2 x 1000 = 2000 µA
(ii) 0.4 A = 0.4 x 1000 = 400 mA = 400 x 1000 = 400,000 µA
(iii) 0.005 mA = 0.005 x 1000 = 5 µA
5.
Current
Value
I3
150mA
I4
250mA
I5
250mA
[3]
Homework Questions 2
1.
2.
[3]
a)
All four cells are pointing in the same direction and so will help
each other so the output voltage will be 4 x 1.5 V = 6V
b)
Three cells are pointing in one direction, One cell is pointing the
opposite way effectively cancelling out one of the three cells. The
output voltage will therefore be 2 x 1.5V = 3V.
[2]
(a)
V2 = V - V1 = 9 - 6 = 3
(b)
[1]
Reading in Volts
V
V1
V2
18
12
12
8
6
4
[2]
3.
The circuit is a parallel circuit, in all parallel circuits the voltage drop is
the same across all branches, therefore:
VAB = VCD = 6V
[2]
43
GCSE Electronics.
Unit E1 : Discovering Electronics
4.
VS = 12V
5a.
(i)
1V = 1 x 1000 = 1000 mV
(ii) 0.7 V = 0.7 x 1000 = 700 mV
(iii) 0.02 V = 0.02 x 1000 = 20 m
[3]
(i)
1600 mV = 1600 ÷ 1000 = 1.6 V
(ii) 400 mV = 400 ÷ 1000 = 0.4 V
(iii) 50 mV = 50 ÷ 1000 = 0.05 V
[3]
5b.
V1 = 4.5V
[2]
Homework Questions 3
1.
a.
b.
V 12

 2A
R 6
V  I  R  2  6  12V
I
[2]
Or by inspection - the lamp is the only component with resistance,
therefore all of the voltage available will appear across the lamp
i.e. 12V
[1]
2.
3.
44
a.
R
V
6

 4
I 1.5
[2]
b.
V  I  R  2  10  20V
(a)
V  I  R  5 mA  2k  10V
(b)
R
V
12

 4k
I 3mA
[2]
(c)
I
V
10

 2mA
R 5k
[2]
[2]
[2]
Topic 1.3 – Circuit Concepts.
4.
(a)
(b)
I1 = 6 – 4 = 2mA
I2 = 4 mA
V2 = V1 = 4V
I2 = 6mA
R
V1 = 10 – 6 = 4V
V
6

 1k
I 6mA
[5]
[2]
Now for some examination style questions.
45
GCSE Electronics.
Unit E1 : Discovering Electronics
Examination Style Questions
1.
Here are 4 resistors, labelled A, B, C & D.
Which resistor will dissipate the most power?
Answer : ...................................................
[1]
2.
Some of the currents flowing in the circuit below have been labelled.
Write down the value of the following currents:
a.
I3 = .......................... mA
b.
I4 = .......................... mA
c.
I5 = .......................... mA
[3]
46
Topic 1.3 – Circuit Concepts.
3.
The normal current and voltages for four bulbs, A,B, C & D are listed in the
following table.
Bulb
A
B
C
D
(a)
Voltage
(V)
6
2.5
6
2.5
Current
(A)
0.1
0.1
0.2
0.2
Which bulb A, B, C or D will use the most power ?.....................................
[1]
(b)
Calculate the power used by bulb B.
.............................................................................................................................
.............................................................................................................................
[1]
4.
Put the following in order of size, starting with the smallest unit.
amp (A)
microamp (µA)
milliamp (mA)
[2]
47
GCSE Electronics.
Unit E1 : Discovering Electronics
5.
Look at the following diagram.
Write down the values of the following:
a.
I1 = .......................... mA
b.
I2 = .......................... mA
c.
V1 = ......................... V
[3]
6.
The current and voltages for four bulbs, A, B, C & D are listed in the following
table.
Bulb
A
B
C
D
(a)
Voltage
(V)
6
6
9
9
Current
(mA)
200
100
200
100
Which bulb A, B, C or D will use the most power ?.....................................
[1]
(b)
Calculate the power used by bulb D. Write the correct unit in the space
provided.
.............................................................................................................................
.................................................................................unit ....................................
[3]
48
Topic 1.3 – Circuit Concepts.
7.
Look at the following diagram.
Write down the values of the following:
8.
a.
I1 = .......................... mA
b.
I2 = .......................... mA
c.
V1 = ......................... V
d.
V2 = ......................... V
The current and voltage ratings for four bulbs, A, B, C & D are listed in the
following table.
Bulb
A
B
C
D
(a)
Voltage
(V)
9
12
9
6
Current
(A)
0.1
0.2
0.2
0.2
Which bulb A, B, C or D will use the least power ?.....................................
[1]
(b)
Calculate the power used by bulb C.
.............................................................................................................................
.............................................................................................................................
[2]
49
GCSE Electronics.
Unit E1 : Discovering Electronics
9.
Here are four units used in electronics:
ohm,
watt,
volt,
amp
(a)
Which one is the unit of current?
.................................
(b)
Which one is the unit of resistance?
.................................
(c)
Which one is the unit of power?
.................................
[3]
10.
The normal current and voltage ratings for four bulbs, A, B, C & D are listed in the
following table.
Bulb
A
B
C
D
Voltage
(V)
12
6
6
12
Current
(A)
0.1
0.1
0.2
0.2
(a)
Which bulb A, B, C or D will use the least power ?
(b)
Calculate the power used by bulb A.
................................
[1]
.............................................................................................................................
.............................................................................................................................
[2]
(c)
The current through bulb C is 0.2A. What value is this in mA?
.............................................................................................................................
[1]
50
Topic 1.3 – Circuit Concepts.
11.
Here are three measures of voltage:
millivolt (mV)
volt (V)
microvolt (µV)
Put these in order of size, starting with the smallest, and ending with the biggest.
[2]
12.
Which one of the signals A, B, C or D is a digital signal?
Answer ............................................
[1]
51
GCSE Electronics.
Unit E1 : Discovering Electronics
13.
Look at the following diagram.
Write down the values of the following:
I1 = .......................... mA
I2 = .......................... mA
I3 = .......................... mA
V1 = ......................... V
14.
The diagram shows part of a circuit.
I
3
R = 2k
R
1
3
I = 5 mA
R2
1
I
4
I5
I = 2 mA
2
(a)
Which statement, A, B or C is true about I5?
A. I5 is bigger than 5mA.
B. I5 is equal to 5mA.
C. I5 is smaller than 5mA.
Answer ………………..
[1]
(b)
Write down the value of current I4.……………………
[1]
(c)
What is the value of current I3. ………………………
[1]
(d)
Which is the bigger resistor, R2 or R3? ..............................
Give a reason. …………………………………………………………………
………………………………………………………………………………………… [1]
(e)
Calculate the voltage across resistor R1.
…………………………………………………………………………………………
…………………………………………………………………………………………
52
[2]
Topic 1.3 – Circuit Concepts.
Self Evaluation Review
Learning Objectives
My personal review of these objectives:



recognise standard symbols for components
included within the module;
apply the current at a junction rule;
apply the voltage divider rule;
explain how voltage at a point can be indicated
relative to a 0V reference;
appreciate that resistance is the opposition to
current flow and that is measured in ohms;
understand the relationship between current,
voltage and resistance in qualitative terms;
select and use
R
V
I
;
recognise that analogue signals are
continuously varying and digital signals are two
state;
state the power is dissipated when current
flows through resistance and is measured in
watts;
understand the relationship between current,
voltage and power in qualitative terms;
perform calculations involving
P V  I ;
recognise and use the following multiple and
sub-multiple indicators: p, n, µ, m, k, and M.
Targets:
1.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
2.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
53