ELECTRICAL CIRCUITS - GR11 & 12 by Lizelle Swanepoel

What is electricity?

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THREE PARAMETERS IN ELECTRICITY

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HOW TO CALCULATE TOTAL RESISTANCE IN SERIES VS PARALLEL

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Voltage drop across a resistor

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YOUR "I CAN" LIST

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This is your I CAN list to reflect on your learning on this section:

Check each point on the white list below and make sure you can do each.
If you are still unsure of a sub-section, establish your mastery doing the following:
- revisit that section in the Notes
- re-watch my posted teaching Videos on Classroom and YouTube
- do Past Papers

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Formulae

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Weighting of ELECTRIC CIRCUITS - Paper 1

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Ammeters and Voltmeters

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An ammeter measures current in a circuit.

An ammeter has VERY LITTLE RESISTANCE.
An ammeter is always connected in SERIES with components in a circuit, as it must allow all the current to flow through it in order to measure current.

A Voltmeter measures potential difference between two points in a circuit.

A voltmeter has GREAT RESISTANCE.
A Voltemeter must therefore always be connected in parallel with a component in a circuit, in order to measure the difference in potential energy between two points right before and after a resistor.

INTERNAL RESISTANCE

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Watch this video.

RESISTORS ADDED INTO A CIRCUIT

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When resistors are added in series, the total resistance increases.
When resistors are added in parallel, the total resistance decreases.
When a load is connected to a battery, the voltmeter connected across the battery will be the reading for 𝑉 𝑒𝑥𝑡.

WITH INTERNAL RESISTANCE IN THE BATTERY:

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If more resistors are added in series:

1. The total resistance (𝑅_T ) increases.
2. The current in the main circuit will decrease, since the emf of the battery remains constant. (I ∝ 1/R)
3. V_lostwill decrease, since the internal resistance remains constant. (V_lost= Ir)
4. V_ex_twill increase, since the emf remains constant. (by Emf = V_ext+ V_lost)

If more resistors are added in parallel:

Total resistance decreases.
Current in mains and through the battery increases.
V _lost increases. (V_lost= Ir)
V_extwill decrease since emf stays constant. (by Emf = V_ext+ V_lost)

Graphs:

In the graph of V_ext (measured across battery) vs 𝐼 (measured in a series part of the external main circuit), the emf of the battery is given by the y-intercept (when the load current is 0 A).

PAST PAPERS (2015-2019)

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(Open this doc on iPad or laptop)

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2015 SUP

INTERNAL RESISTANCE PRAC

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To determine the internal resistance of a battery of cells:

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Consider the equation below:

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Rearrange the equation into the form of a straight line graph to match the quantities plotted on the graph.

Rearranged into y = mx + c form:

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Emf = V_ext + Ir
V_ext = -rI + Emf
(y = mx + c)

Where: y-int = Emf
m = - r
x = I

What is the maximum current which can be delivered by the battery?

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For max current (off the graph), V_ext = 0.
Hence:

V_ext = -rI + Emf
0 = -rI + Emf
Emf = rI
I = Emf / r
= y-int / gradient

SUMMARY ON INTERNAL RESISTANCE

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FURTHER CIRCUIT PROBLEMS - HOW TO SOLVE

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GENERAL MISCONCEPTIONS ABOUT SIMPLE CIRCUITS

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Students sometimes fail to discriminate between these terms and concepts:

Potential difference:
- emphasizes that we are measuring a change in “push” between two different points in an electric circuit.
Electromotive force (emf):
- a term for 'voltages' across sources of electrical energy.
Cells becoming 'discharged'
- charge is not used up, energy is transferred.
Conventional current:
- This flows (by definition) from positive to negative around the external circuit
- Inside the cell chemical reactions ‘pump’ charge carriers to the terminals.
- Some may say that ‘physicists got it wrong because we now know that electrons flow the other way.’
- But it is really an arbitrary choice.
- One can illustrate this by looking at current flow and movement of charge carriers in an electrolyte (or an ionized gas).
- Positive ions go one way, negative ions go the other way.
- And so, however current is defined, there are always examples where current direction and charge carrier movement are opposite.

Current flows all around a circuit:
- including through the cell itself.

Analogy for charge flow is a bicycle Chain:
- This transfers energy from you (equivalent to the cell) to the rear wheel.
- The chain is not used up (neither is charge),
- and does not disappear when you run out of energy (when the cell runs flat and the chemical reactions within it stop).
- It has no beginning and no end.
- It moves as a SYSTEM, every part all at once.
- this is the CYCLIC SIMULTANEOUS MODEL OF ELECTRIC CIRCUITS.

Another analogy:
- Skiers (charges) being lifted up a mountain by a ski lift (external energy source/emf/cell) and then skiing down a slope (resistor).
- This is useful for the idea of voltages in parallel circuits.
- Parallel slopes drop different skiers through the same vertical height (equal voltages across components in parallel).

CALCULATIONS USING OHM’S LAW

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Series-parallel circuits Recap

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Watch this video on worked examples

The Magic of Electricity

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“La Dame de Fer” all aglow.

Electrical lighting facts about the Eiffel Tower

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Number of lightbulbs = 20 000
Power of each bulb = 6 W
Length of cabling = 40 km
The Eiffel starts twinkling:

every day, from 10 pm to 1am

Just for laughs

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THEORY RECAP

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CELLS IN SERIES VS PARALLEL

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CURRENT FLOW IN METALS

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Metals consist of positive ions surrounded by a “sea” of delocalised electrons.

The delocalised electrons are free to move through the crystal structure.
When connected to a power source, the electrons all drift in the same direction which creates an electric current (flow of charge at a certain rate).

CURRENT

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Current = The rate of flow of charge between two points in a circuit.

VOLTAGE

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Voltage = Electrical energy transferred per unit positive charge between two points in a circuit.

VOLTAGE = The "PUSH" behind the charge in the circuit.
EMF = The total energy supplied per unit positive charge by the cell.

RESISTANCE

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Resistance = A material’s opposition to the flow of current through it.

The factors that affect resistance of a resistor:

Length
Thickness
Temperature
Type of material (resistivity)

State the relationship between resistance and each of these factors, and give a reason for each relationship.

RESISTORS - DIFFERENT TYPES

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1. Fixed resistors

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2. Variable resistor (rheostat)

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3. Potentiometer (another type of variable resistor)

RELATIONSHIP BETWEEN I, V and R

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Current through a conductor is directly proportional to potential difference across a conductor, provided the temperature of the conductor stays constant.
Therefore:
R = V/I

OHM'S LAW EXPLAINED

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VERIFYING OHM'S LAW

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EXPERIMENT

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WHICH EQUATION TO USE?

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RESISTOR SYMBOLS

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EXERCISE 1 - HOMEWORK ANSWERS

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EXAMPLE

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EXAMPLE SOLUTIONS

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CHECK POINT

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DO THIS PROBLEM

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HOW TO ANALYSE A CIRCUIT USING THE COLOUR CODING TECHNIQUE

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Red = High electrical potential
Blue = Low electrical potential

EXAM STYLE QUESTION

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HOW TO USE THIS PADLET

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Magnify posts by clicking ctrl+ on your computer
Reduce posts by clicking ctrl- on your computer
Watch all posted videos in the Padlet to assist learning this section
Watch all my posted teaching videos on Classroom as overview of each topic
Download PhET's DC Kit virtual Lab to physically build circuits yourself given to you in harder problems to assist understanding of circuit rules.

ELECTRIC POTENTIAL COLOUR CODING TECHNIQUE

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Watch this video:

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TRY THIS CIRCUIT

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R4 is shorted out the circuit. No current passes through R4.

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COST OF ELECTRICITY USAGE

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Electrical energy consumed is measured in kilowatt hours (kWh).

1 kWh refers to the use of 1 kW of electricity for 1 hour.
1 kWh is equivalent to 3 600 000 J of electrical energy:
1 kWh = 1 000 W × 1 h = 1 000 W × 3 600 s = 3 600 000 J

Electrical consumption is charged per kWh used.

EXAMPLE 1:
Suppose a 1100 W electrical iron is used for 4 hours and the cost of electrical energy is 61c per kWh. What is the cost of using the iron for 4 hours?

Cost = Power rating of appliance (in kW) × time used (in hours) × price per kWh

= 1,1 kW × 4 hours × 61c = 268,4c = R 2,68

EXAMPLE 2:

An electric kettle has a power output of 2,2 kW 240 V.

a) Calculate the current in the kettle.

b) Calculate the resistance of the kettle element.

c) Calculate the cost of using the kettle for 5 hours if the cost per kWh is 61c.

ENERGY vs. POWER

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Energy = the ability to do work.

Power = the rate at which work is done/the rate at which electrical energy is transferred between two points in a circuit.

ENERGY IN A CIRCUIT

A cell forces charge to move in a complete circuit.
The charge is supplied with electrical energy in the cell as a result of chemical reactions that take place inside the cell.
As the charge passes through each component in the circuit, work (W) is done by the cell to drive charge through the component
Electrical energy is converted into other forms of energy in circuit elements.
We say that electrical energy is dissipated in a resistor (converted to other energy forms).
E = W
- The work done (W) in moving the electric charge between the ends of a resistor is equal to the energy dissipated in the resistor.
- The symbol for electrical energy will also be W.
- It is measured in Joules (J) as the unit.

HEATERS CONVERT ELECTRICAL ENERGY INTO HEAT ENERGY

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INCANDESCENT LIGHTBULB FILAMENT

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It converts electrical energy into heat energy

ELECTRICAL ENERGY DISSIPATED IN A CIRCUIT ELEMENT (RESISTOR)

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Deriving three equations for electrical energy from fundamental principles:

POWER DISSIPATED IN A RESISTOR/DELIVERED BY A BATTERY

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Derive these formulae

JOSEPH SWAN

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Inventor of the first carbon filament evacuated light bulb - one year before Edison.

COMMERCIALIZING ELECTRICITY

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WATCH THIS VIDEO

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POWER

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James Watt invented the steam engine and coined the unit for power as the Watt.

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TOASTERS CONVERT ELECTRICAL ENERGY INTO HEAT ENERGY

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BRIGHTNESS OF A BULB DEPENDS ON THE POWER DELIVERED TO IT

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Explain this:

CHECK POINT ON ELECTRICAL ENERGY - DO THIS PROBLEM:

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A torch bulb uses two 1,5 V cells connected in series. The bulb has a resistance of 16,3 Ω.

a) Calculate the electrical energy dissipated in the torch bulb in 5 minutes.

b) Calculate the current in the torch bulb.

c) Suppose the same bulb is connected to another battery (for the same length of time) so that the current in the torch bulb is doubled. By what factor would the amount of electrical energy dissipated in the bulb change?

POWER RATINGS

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The power value written on any device is the rate at which it can convert electrical energy into other forms of energy.
A value of say 20W means that 20J of energy is converted per second.

POWER - WORKED EXAMPLE

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An electric kettle is rated at 2,2 kW, 240 V. The supply voltage is reduced from 240V to 230V. Calculate the new power of the kettle.

SUMMARY

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HOMEWORK

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p71-75

INTERNAL RESISTANCE

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INTERNAL RESISTANCE

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CHECKPOINT 14

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A cell of unknown emf and internal resistance is connected in series with a 16 Ω resistor and a voltmeter connected across the resistor reads 1,2 V. When the 16 Ω resistor is replaced with an 8Ω resistor, the voltmeter reads 1 V.

a) Draw a neat circuit diagram and explain why the voltmeter reading decreased when the resistance was decreased.

b) Calculate the emf and internal resistance of the cell.

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PRACTICAL - MEASURING INTERNAL RESISTANCE

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NOTE:

EMF = Voltage across battery when the circuit is open (I=0).
Terminal PD = Voltage across battery when charge is flowing through it.

WHAT IS "AMP-HOURS"?

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WATT-HOURS

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SUMMARY OF VOLTAGE, CURRENT, AC VS DC, POWER, WATT-HOURS, CALCULATING WATT-HOUR RATING OF A BATTERY, PARALLEL-SERIES CONNECTIONS

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This video is brilliant - make sure to watch it!

HOMEWORK

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Pages 76-78, page 80, pages 82-84.

MATRIC PORTFOLIO PRAC - DETERMINING THE INTERNAL RESISTANCE OF A BATTERY:

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PROBLEM

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They repeat the above steps for different sliding contact positions and tabulate the readings:

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How can a graph of data be more informative than a table of the same data?

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A graph provides a visual informational view instead of simply numbers on a table.
Some of the numbers may be anomalies, and using them in a formula will increase the percent error from the accepted value.
The more data collected, the more points can be plotted on the graph for a more accurate line of best fit.
It presents a more accurate value of the metric you want to calculate.

ANSWERS TO ALL EXERCISES AND WORKED EXAMPLES

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THREE PARAMETERS IN ELECTRICITY

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ELECTRICAL ENERGY

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Thomas Edison commercialized electricity, which we still pay for today, per kiloWatt-hour (kWh).