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)