75
DC Circuits
DC Circuits
Topics
1. Circuit Symbols2. 5 principles of DC Circuits3. 2 tips for solving DC Circuits4. 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 light-sensitive 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?
A
AAmmeter Reading = 0.2 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?
I0.3 A
0.2 A
Worked Example 3
• What is the value and direction of current in wire X?
0.2 A
0.3 A
0.2 A
X
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 VV
V
3.0 V
Voltmeter Y
1.0 VVoltmeter X
Worked Example 5
• What is the reading of voltmeter X?
V V
V
Voltmeter X
4.5 V
1.0 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
V
Voltmeter X
4.0 V
Worked Example 7
• What is the reading of voltmeter X?
V
V
Voltmeter X
4.0 V
V
1.0 V
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?
1 Ω 1 Ω
V
3 V
Worked Example 9
• What is the reading of the voltmeter?
1 Ω 2 Ω
V
3 V
Worked Example 10
• What is the reading of the voltmeter?
3 Ω 4 Ω
V
5 V
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.
R R
10 V
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
R
V
R/2 R/2
50 cm 50 cm
V
Worked Example 11
• What is the reading of the voltmeter?
V
30 cm 70 cm
5 V
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.
100 cm
5 V
0 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
R
Is the same as
Shorting Components
R R
R
R
Is the same as
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
3 Ω
2 Ω
2 Ω
convert to 4 Ω
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)
