Chapter 20 DC Circuits
Chapter 20 DC Circuits
Chapter 20 DC Circuits
PHYSICS
D.C. CIRCUITS
LEARNING OUTCOMES
NUMBER
LEARNING OUTCOME
ii
iii
L e a r n K i r c h o f f s 1 st a n d 2 nd L a w s .
iv
U s e K i r c h o f f s L a w s t o f i n d e q u i v a l e nt r e s i s t a n c e s f o r
series and parallel combinations.
L e a r n h o w t o a p p l y K i r c h o f f s L a w s a n d e q u i va l e nt
resistances to solve simple circuit problems.
vi
vii
viii
What is a potentiometer?
ix
CIRCUITS
A circuit is a connection of circuit
elements, connected in series or
parallel arrangements , that allow for
the flow of current in a complete
path.
A source of e.m.f. usually drives
current through the circuit (as
learned in the previous chapter).
CIRCUIT ELEMENTS
Table 9.1, page 129, Chapter 9:
Electric Current, Potential
Difference and Resistance;
Cambridge International AS
and A Level Physics
Coursebook, Sang, Jones,
Chadha and Woodside, 2nd
edition, Cambridge University
Press, Cambridge, UK,2014.
CIRCUIT ELEMENTS
Table 9.1, page 129, Chapter
9: Electric Current, Potential
Difference and Resistance;
Cambridge International AS
and A Level Physics
Coursebook, Sang, Jones,
Chadha and Woodside, 2nd
edition, Cambridge University
Press, Cambridge, UK,2014.
CIRCUIT ELEMENTS
The symbols listed in the previous two
slides are symbols of commonly
encountered circuit elements.
These symbols should be learned by
heart by the student to enable ease of
reading of the circuit, and more
importantly, how each circuit element
behaves in a circuit.
KIRC HOF F S
ST
1
LAW
KIRC HOF F S
ST
1
LAW
KIRC HOF F S
ST
1
LAW
EXAMPLES
Figure 7.17: Example , Page 178, Chapter 7: Electricity, International A/AS Level Physics,
by Mee, Crundle, Arnold and Brown, Hodder Education, United Kingdom, 2008.
EXAMPLES
Figure 7.18: Question 1 , Page 178, Chapter 7: Electricity, International A/AS Level
Physics, by Mee, Crundle, Arnold and Brown, Hodder Education, United Kingdom,
2008.
EXAMPLES
Figure 7.19: Question 2 , Page 178, Chapter 7: Electricity, International A/AS Level
Physics, by Mee, Crundle, Arnold and Brown, Hodder Education, United Kingdom,
2008.
KIRC HOF F S
ND
2
LAW
KIRC HOF F S
ND
2
LAW
KIRC HOF F S
ND
2
LAW
KIRC HOF F S
ND
2
LAW
KIRC HOF F S
ND
2
LAW
Figure 10.9, page
146, Chapter 9:
Electric Current,
Potential
Difference and
Resistance;
Cambridge
International AS
and A Level Physics
Coursebook, Sang,
Jones, Chadha and
Woodside, 2nd
edition, Cambridge
University Press,
Cambridge,
UK,2014.
KIRC HOF F S
ND
2
LAW
KIRC HOF F S
ND
2
LAW
KIRC HOF F S
ND
2
LAW
R ESISTORS IN SE R IES
We can use Kirchoffs 2nd Law to find the
formula to calculate the total resistance
of two or more resistors connected in
series.
Figure 10.16, page 148, Chapter 9: Electric Current, Potential Difference and
Resistance; Cambridge International AS and A Level Physics Coursebook, Sang,
Jones, Chadha and Woodside, 2nd edition, Cambridge University Press, Cambridge,
UK,2014.
R ESISTORS IN SE R IES
In the previous slide, R1 and R2 are two
resistors connected in series.
The current flowing through both resistors is
equal.
We will use Kirchoffs 2nd Law to obtain a
formula to find the total resistance of the
three resistors in series.
R ESISTORS IN SE R IES
If we apply a potential difference of V across
the 2 resistors, V1 + V2 + = V, based on
Kirchoffs 2nd Law.
Hence, V = IR1 + IR2 = I(R1 + R2); or
.
But,
.
Hence,
.
R ESISTORS IN SE R IES
What this tells us is that the total resistance of
all resistors connected in series is equal to the
sum of all the individual resistances.
This derivation can be extended to be used for
more that 2 resistors in series by deduction.
R ESISTORS IN SE R IES
We can use Kirchoffs 1st Law to find
the formula used to calculate the
total resistance of two or more
resistors connected in parallel.
R E S I S TO R S I N PA R A L L E L
Figure 10.18, page 149, Chapter 9: Electric Current, Potential Difference and
Resistance; Cambridge International AS and A Level Physics Coursebook, Sang,
Jones, Chadha and Woodside, 2nd edition, Cambridge University Press, Cambridge,
UK,2014.
R E S I S TO R S I N PA R A L L E L
The diagram on the previous slide shows two
resistors, R1 and R2 connected in parallel.
The potential differences across the 2
resistors will be equal.
We will use Kirchoffs 1st Law to find the total
resistance.
R E S I S TO R S I N PA R A L L E L
The total current, based on
Kirchoffs 1st Law.
Hence,
; or,
R E S I S TO R S I N PA R A L L E L
This tells us that the inverse of the total
resistance of resistive elements connected in
parallel is equal to the sum of the inverses of
all the resistances that are connected in
parallel.
This proof can be extended for more than 2
resistors in a parallel combination by
deduction.
EXAMPLES
Figure 7.28: Example, Page 186, Chapter 7: Electricity, International A/AS Level
Physics, by Mee, Crundle, Arnold and Brown, Hodder Education, United Kingdom,
2008.
EXAMPLES
Figure 7.29: Question 1, Page 187, Chapter 7: Electricity, International A/AS Level
Physics, by Mee, Crundle, Arnold and Brown, Hodder Education, United Kingdom,
2008.
EXAMPLES
Figure 7.29: Question 2, Page 187, Chapter 7: Electricity, International A/AS Level
Physics, by Mee, Crundle, Arnold and Brown, Hodder Education, United Kingdom,
2008.
EXAMPLES
May/June 2008, Paper 1, question 37.
EXAMPLES
May/June 2008, Paper 2, question 6.
EXAMPLES
May/June 2008, Paper 2, question 6 (contd).
EXAMPLES
May/June 2008, Paper 2, question 6 (contd).
EXAMPLES
May/Jun 2009, Paper 21, question 7.
EXAMPLES
May/Jun 2009, Paper 21, question 7 (contd).
EXAMPLES
May/Jun 2009, Paper 21, question 7 (contd).
EXAMPLES
May/Jun 2009, Paper 21, question 7 (contd).
EXAMPLES
May/Jun 2009, Paper 21, question 7 (contd).
EXAMPLES
Oct/Nov 2010, Paper 12, question 35.
EXAMPLES
May/June 2011, Paper 11, question 36.
EXAMPLES
Oct/Nov 2011, Paper 12, question 36.
HOMEWORK
1.
2.
3.
4.
5.
6.
7.
8.
HOMEWORK
9.
10.
11.
12.
13.
14.
15.
16.
HOMEWORK
17.
18.
19.
20.
21.
22.
23.
24.
HOMEWORK
25.
26.
27.
28.
29.
30.
31.
32.
HOMEWORK
33. Oct/Nov 2012, Paper 13, question 37.
34. Oct/Nov 2012, Paper 23, question 4.
Figure 12.6, page 172, Chapter 12: Practical Circuits; Cambridge International AS and
A Level Physics Coursebook, Sang, Jones, Chadha and Woodside, 2nd edition,
Cambridge University Press, Cambridge, UK,2014.
Figure 7.31: Page 187, Chapter 7: Electricity, International A/AS Level Physics, by
Mee, Crundle, Arnold and Brown, Hodder Education, United Kingdom, 2008.
;
Note that at all instances.
T HE R MISTORS
Thermistors are resistive elements
whose resistivity is effected by its
temperature.
Thermistors are represented by the
symbol
We will only look at negative
temperature coefficient thermistors; i.e.
thermistors that the values of resistivity
decrease when the temperature
increases.
T HE R MISTORS
Since the resistance of a resistor that has
fixed length and cross sectional area is
linearly proportional to its resistivity, the
resistance of a thermistor will also
decrease with increase in temperature.
For thermistors, the resistance is higher
at lower temperatures, and the
resistance decreases exponentially with
increase in its temperature as seen in
the graph on the next slide.
T HE R MISTORS
The curve on
the left shows
the resistance
vs.
temperature
curve of a
negative
temperature
coefficient
thermistor.
Figure 11.10, page 172, Chapter 11: Resistance and Resistivity; Cambridge
International AS and A Level Physics Coursebook, Sang, Jones, Chadha and Woodside,
2nd edition, Cambridge University Press, Cambridge, UK,2014.
T HE R MISTORS
Thermistors are often connected in series
with a fixed resistor to form a potential
divider circuit.
By varying the temperature of the
thermistor, we can get different potential
differences across the fixed resistor and
thermistor.
This can be used in a fire alarm, for
example.
EXAMPLES
EXAMPLES
Figure 7.35,
Question 1: Page
190, Chapter 7:
Electricity,
International
A/AS Level
Physics, by Mee,
Crundle, Arnold
and Brown,
Hodder
Education,
United Kingdom,
2008.
EXAMPLES
Figure 7.35,
Question 1: Page
190, Chapter 7:
Electricity,
International
A/AS Level
Physics, by Mee,
Crundle, Arnold
and Brown,
Hodder
Education,
United Kingdom,
2008.
EXAMPLES
May/June 2008, Paper 1, question 36.
EXAMPLES
Oct/Nov 2008, Paper 2, question 7.
EXAMPLES
Oct/Nov 2008, Paper 2, question 7 (contd).
EXAMPLES
Oct/Nov 2008, Paper 2, question 7 (contd).
EXAMPLES
Oct/Nov 2008, Paper 2, question 7 (contd).
EXAMPLES
Oct/Nov 2008, Paper 2, question 7 (contd).
EXAMPLES
Oct/Nov 2010, Paper 22, question 6.
EXAMPLES
Oct/Nov 2010, Paper 22, question 6 (contd).
EXAMPLES
Oct/Nov 2010, Paper 22, question 6 (contd).
EXAMPLES
Oct/Nov 2010, Paper 22, question 6 (contd).
EXAMPLES
Oct/Nov 2010, Paper 22, question 6 (contd).
EXAMPLES
Oct/Nov 2010, Paper 22, question 6 (contd).
EXAMPLES
Oct/Nov 2010, Paper 22, question 6 (contd).
HOMEWORK
1.
2.
3.
4.
5.
6.
7.
8.
HOMEWORK
9.
10.
11.
12.
13.
14.
15.
16.
HOMEWORK
17. Oct/Nov 2012, Paper 12, question 38.
18. Oct/Nov 2012, Paper 22, question 5.
POT E NT IOME T E RS
A potentiometer can be set up by using a
piece of resistance wire, and the ends are
connected across a known source of
e.m.f (the driver cell).
A potentiometer is an device that can be
used to compare p.d.s or e.m.f.s to
obtain unknown e.m.f.s or p.d.s
POT E NT IOME T E RS
The diagram on the following slide shows
how a potentiometer may be used to
determine the unknown e.m.f on a cell.
POT E NT IOME T E RS
Figure 12.8, page 172, Chapter 12: Practical Circuits; Cambridge International AS and
A Level Physics Coursebook, Sang, Jones, Chadha and Woodside, 2nd edition,
Cambridge University Press, Cambridge, UK,2014.
POT E NT IOME T E RS
Point Y is where the jockey is in contact
with the conductor AB.
By moving the position of the jockey, we
can vary the p.d.s and since
p.d.s across both sections are directly
proportional to the lengths of each
section.
POT E NT IOME T E RS
Recall that the p.d. across the resistive
element is directly proportional to its
resistance, and the resistance of a
resistive element is directly proportional
to its length.
Hence, this is why p.d. across a resistive
element is directly proportional to its
length.
POT E NT IOME T E RS
To obtain the e.m.f. of cell X, we move
the jockey along the length of AB until
the reading of the galvanometer = 0.
We need to record the length of AY, .
When this occurs, the p.d. across AY,
e.m.f.
of cell X, ! .
!
"
"
POT E NT IOME T E RS
The following few slides explain a better
method to obtain the value of an
unknown e.m.f.
This is because we need to take into
account the internal resistance of " .
If #%
has an internal resistance,
$ " , since is now the
terminal p.d. of " .
POT E NT IOME T E RS
Figure 12.9, page 173, Chapter 12: Practical Circuits; Cambridge International AS and
A Level Physics Coursebook, Sang, Jones, Chadha and Woodside, 2nd edition,
Cambridge University Press, Cambridge, UK,2014.
POT E NT IOME T E RS
The diagram on the previous slide shows
how to set up a potentiometer to obtain
the an unknown #( .
This method employs two known e.m.f.s,
#% and #) .
#) is used first to obtain the length of
section AD, &' .
POT E NT IOME T E RS
#( is then used first to obtain the length
of section AC, &* .
From your understanding of the
relationships between lengths and p.d.s,
we will obtain the relationship
+
,
EXAMPLES
Figure 7.34:
Example 2, Page
189, Chapter 7:
Electricity,
International
A/AS Level
Physics, by Mee,
Crundle, Arnold
and Brown,
Hodder
Education, United
Kingdom, 2008.
EXAMPLES
Oct/Nov 2008, Paper 1, question 37.
EXAMPLES
Oct/Nov 2010, Paper 11, question 37.
EXAMPLES
May/June 2011, Paper 11, question 37.
EXAMPLES
May/June 2011, Paper 21, question 5.
EXAMPLES
May/June 2011, Paper 21, question 5 (contd).
EXAMPLES
May/June 2011, Paper 21, question 5 (contd).
EXAMPLES
May/June 2011, Paper 21, question 5 (contd).
EXAMPLES
May/June 2011, Paper 21, question 5 (contd).
EXAMPLES
May/June 2011, Paper 21, question 5 (contd).
EXAMPLES
May/June 2011, Paper 21, question 5 (contd).
HOMEWORK
1.
2.
3.
4.
5.
6.
7.