DC Circuits
Topics
1.
2.
3.
4.
Circuit Symbols
5 principles of DC Circuits
2 tips for solving DC Circuits
Putting it all together – Electricity Problem
Solving Toolkit
CIRCUIT SYMBOLS
Circuit Symbols (pg 324)
• Sources of E.M.F.:
– Cell & Battery
– D.C. Power Supply
– A.C. Power Supply
• Resistor
– Fixed Resistor
– Variable Resistor
(Rheostat)
– Light Dependent Resistor
(LDR)
– Thermistor
– Light Emitting Diode (LED)
• Meters
– Ammeter
– Voltmeter
•
•
•
•
•
Switch
Light Bulb (Lamp)
Fuse
Bells
Variable Potential Divider
(Potentiometer)
Cell (Battery)
D.C. Supply
A/C Supply
Fixed Resistor
Variable Resistor (Rheostat)
Light Dependent Resistor (LDR)
• LDRs decrease their
resistance when
exposed to light
• Often used as
components for lightsensitive circuits (e.g.
turn on lamps when it is
dark)
Thermistor
• Thermistors decrease
resistance when
exposed to heat
Semiconductor Diode
• Allows current to flow
in one direction
• Blocks current in
opposite direction
Light Emitting Diode (LED)
• Same as a diode, except
now it emits light when
current is flowing in the
allowed direction
Potentiometer
• Also called “variable
potential divider”
• Is actually just a wire
attached to a metre rule
• Comes with an
apparatus called a
“jockey”
• Will use this in the lab
to prepare for SPA 2
Ammeter
Voltmeter
Galvanometer
Switch
Light Bulb
Fuse
Bell
Earth
Transformer
ELECTRICITY PROBLEM SOLVING
TOOLKIT
Toolkit
• A handyman has a toolbox with many tools
(e.g. hammer, spanner, screwdriver, etc.) In
each situation he won’t need to use ALL his
tools, but different situations call for different
tools.
• Similarly, when solving electricity problems
there is a total of 11 tools you can use. You
won’t need to use ALL your tools for any one
question, but different questions call for
different tools.
Electricity Problem Solving Toolkit
4 equations
• Definition of Current
• Definition of Resistance
• Electrical Power
• Electrical Energy
2 arrangements of Resistors
• In series
• In parallel
5 Principles
• Current in Series
• Current in Parallel
• P.d. in series
• P.d. in parallel
• Potential Divider
3 tips
• check for short circuit
• redraw diagram
• replace cluster of resistors
Equations
• Definition of Current
• I = Q/t
• Definition of Resistance
• R = V/I
Arrangement of Resistors
• In series
• Rtotal = R1 + R2 + R3 +….
• In parallel
• 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ….
• 2 parallel resistors only (optional)
• Rtotal = (R1R2)/(R1 + R2)
Electricity Problem Solving Toolkit
4 equations
• Definition of Current
• Definition of Resistance
• Electrical Power
• Electrical Energy
2 arrangements of Resistors
• In series
• In parallel
5 Principles
• Current in Series
• Current in Parallel
• P.d. in series
• P.d. in parallel
• Potential Divider
3 tips
• check for short circuits
• redraw diagram
• replace cluster of resistors
5 PRINCIPLES OF DC CIRCUITS
Current in Series
• In a series circuit (i.e. no parallel circuits), the
current is the same at all points of the circuit
Worked Example 1
• What is the reading of Ammeter X?
Ammeter
Reading =
0.2 A
A
A
Ammeter X
Practice Task
• GLM Pg 307 2(b), Pg 308 Qn 3(a)
Current in Parallel
• In a parallel circuit, there must be branches
• Current follows the “what goes in must come
out” rule
Worked Example 2
• What is the value of I?
I
0.3 A
0.2 A
Worked Example 3
• What is the value and direction of current in
wire X?
0.2 A
0.2 A
X
0.3 A
Practice Task
• GLM Pg 311 Qn 1(b)
• Pg 320 Qn 1
Potential Difference in Series
• Total p.d. is equals to the sum of the individual
p.d. components across the series
• This is similar to calculating resistance of
resistors in series
• Note that p.d. across wire (without resistors)
is zero
Worked Example 4
• What are the readings of voltmeters X and Y?
V
3.0 V
V
Voltmeter X
V
Voltmeter Y
V
1.0 V
Worked Example 5
• What is the reading of voltmeter X?
V
V
1.0 V
Voltmeter X
V
4.5 V
Practice Task
• GLM Pg 307 Qn 2(a), Pg 308 3(b)
Potential Difference in Parallel
• p.d. is the same across parallel branches
Worked Example 6
• What is the reading of voltmeter X?
V
4.0 V
V
Voltmeter X
Worked Example 7
• What is the reading of voltmeter X?
V
4.0 V
V
V
1.0 V
Voltmeter X
Practice Task
• GLM Pg 312 Qn 4(a)
Multi-tool Practice Tasks
• GLM Pg 311 Qn 1(a), 2(b), 3(a), 3(b)
• Pg 322 Qn 1(a), 1(b)
Quiz 18a
Assignment 18a
• TYS Topic 18
• Paper 1 Qn 2, 4, 11, 15, 18, 19, 22, 24, 31, 32
• Paper 2 Qn 1
Potential Divider Principle
• The ratio of the resistances is the ratio of the
p.d.
• Equation form (not recommended to
memorize):
• V1 = [R1/(R1 + R2)]Vɛ
Worked Example 8
• What is the reading of the voltmeter?
3V
1Ω
V
1Ω
Worked Example 9
• What is the reading of the voltmeter?
3V
1Ω
V
2Ω
Worked Example 10
• What is the reading of the voltmeter?
5V
3Ω
V
4Ω
Practice Task
• GLM Pg 307 Qn 1(b)
• Pg 308 Qn 4(b), 4(c)
How is a potential divider useful?
• Let’s say I only have a 10 V battery, but I only
need 5 V of emf for a circuit. I can use a
potential divider to “divide up” my 10 V
battery into just 5 V. 10 V
R
R
Potentiometer
• However, using resistors to divide up emf is
inflexible. We cannot change the ratio easily
(need to change the resistors manually).
• An easier method is to use a potentiometer
(or variable potential divider)
Potentiometer
50 cm
50 cm
R
V
R/2
V
R/2
Worked Example 11
• What is the reading of the voltmeter?
5V
30 cm
V
70 cm
Worked Example 12
• State and explain what will happen to the
lamp as the jockey slides from the 0 cm mark
to the 100 cm mark.
5V
0 cm
100 cm
Practice Task
• GLM Pg 319 Qn 1(a), 1(b)
• Potential divider circuits may also involve the
use of LDRs and Thermistors
• GLM Pg 319 Qn 2(b), Pg 320 Qn 3(b)
Worked Example 13
• Design a circuit which switches on a lamp
automatically when it turns dark (hint: when
bright, p.d. across lamp is low. when dark, p.d.
across lamp is high)
Quiz 18b
Electricity Problem Solving Toolkit
4 equations
• Definition of Current
• Definition of Resistance
• Electrical Power
• Electrical Energy
2 arrangements of Resistors
• In series
• In parallel
5 Principles
• Current in Series
• Current in Parallel
• P.d. in series
• P.d. in parallel
• Potential Divider
3 tips
• Check for short circuits
• redraw diagram
• replace cluster of resistors
3 TIPS FOR DC CIRCUITS
3 Tips
• The following are not found in most textbooks
• Strictly speaking, these are tips not tools, but
they can be really helpful nevertheless
Tip 1: Checking for Short Circuits
• In theory, a wire has zero resistance
• When a wire bypasses a circuit component, all
the current flows through the wire instead of
the component. This is called “shorting the
component”.
• If a wire shorts ALL the resistors, it is said to
form a “short circuit”, which is very dangerous
in real life since (current becomes very high)
Shorting Components
R
R
Is the same as
R
Shorting Components
R
Is the same as
R
R
R
Short Circuit (very dangerous)
R
R
Is the same as
Tip 2: Redraw Circuit Diagrams
• A helpful habit is to redraw circuit diagrams
such that the arrangement is easy to see:
Arrangement of Resistors
Practice Task
• Redraw the following circuit diagrams
– GLM Pg 312 Qn 4
– Pg 313 Worked Example 2
– Pg 315 Qn 2
Challenge Yourself!
• Redraw the following resistor arrangements:
Tip 3: Replace Resistors in a Cluster
• A short cut for some calculation questions
involve replacing a cluster of resistors with
one resistor of same effective resistance
2Ω
convert to
3Ω
2Ω
4Ω
Practice Task
• GLM Pg 307 Qn 1(a)
• Pg 312 Qn 4(c)
[hint: you have already determined I1 and I2
from earlier parts of question]
Electricity Problem Solving Toolkit
4 equations
• Definition of Current
• Definition of Resistance
• Electrical Power
• Electrical Energy
2 arrangements of Resistors
• In series
• In parallel
5 Principles
• Current in Series
• Current in Parallel
• P.d. in series
• P.d. in parallel
• Potential Divider
3 tips
• check for short circuit
• redraw diagram
• replace cluster of resistors
Assignment 18b
•
•
•
•
TYS Topic 18
Paper 1 Qn 3, 7, 13, 16, 23, 26, 29, 33, 34
Paper 2 Section A Qn 4 except (c)(iii)
Paper 2 Section B Qn 2(a)