Grade 9: Electricity Summary
1- Elements of electric circuits 1-1- Connection rules: a- Series connection:
A M N B (L ) (L ) (L ) 1 2 3
Law of unity of current in series: I1 = I2 = I3 = I.
Law on addition of voltages in series: Utotal =U1 + U2 + U3
Or UAB = UAM + UMN + UNB.
b- Parallel connection: (L ) 1 Law of addition of currents in parallel (L ) (the junction rule): I = I + I + I . 2 total 1 2 3 • • Law on unity of voltage in parallel: A B (L ) 3 UAB = U1 = U2 = U3. 1-2- Types of circuits:
a- Closed circuit: (closed switch) (G) (K) • • - IK = IL = IG ≠0.
- Uk = 0; UL = UG = E.
(L)
(G) (K) • • b- Open circuit: (open switch)
- IK = IL = IG =0.
- UL = 0; UK = UG = E. (L)
c- Short circuit: (when a device is coupled with a connecting wire)
(G)
- Voltage of the device is zero UL =0.
- Current flowing in the device is also zero I = 0. L (L ) (L (All current flows in the wire) 1 2
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Grade 9: Electricity Summary
1-3- Measuring instruments: a- The ammeter: Load (A) - Measures electric current. I COM - Connected in series with the studied device such that the COM is to the negative pole of the dry cell.
b- The voltmeter: Load - Measures voltage. - Connected in parallel across the studied device (V) with the COM along the side of the negative pole COM of the dry cell.
2- The oscilloscope & AC voltage 2-1- The oscilloscope: The oscilloscope is a device used to display the variation of the voltage as a function of time. Its screen is composed of two axes: - X-axis: Used to keep track of time. The scale used on it has a unit “s/div” or
“ms/div” and it is called “horizontal sensitivity” (Sh) or “time base” (Vb). - Y-axis: Used to measure voltage. The scale used on it has a unit “V/div” and it is called “vertical sensitivity”. The oscilloscope has two channels. Each one has A B • two poles: an input “Y” (also called phase or channel) Load and a negative pole “COM” (also known as ground, or earth). When connected as shown in the adjacent com Y figure, the oscilloscope reads the voltage “UAB” (that is from input to com).
In DC mode, the voltage remains constant with time evolution. So, the displayed oscillogram is a horizontal straight line. If the input is connected to the negative pole of the generator, the oscilloscope
displays a negative voltage (the oscilloscope still reads UAB). When there is no voltage across the oscilloscope, it displays a horizontal line confounded with the x-axis.
Voltage is calculated by:
Time, usually period, is calculated by: If time sweep is turned off, no more displacement on the x-axis; but only on y-axis.
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Grade 9: Electricity Summary
2-2- AC voltage: Alternating current is a special signal that keeps on changing intensity and direction of flow. AC-voltage has no polarity and keeps on changing, periodically. Depending on the shape of the signal, some AC voltages are: triangular, square, or alternating sinusoidal… When an appliance functions under an AC voltage, it receives a constant value which produces (mathematically) the same energy. This DC-value is called
“effective voltage” (Ue). In AC mode, a voltmeter measures the effective voltage. (Ammeter measures effective current). The effective voltage can be calculated only for alternating sinusoidal voltage. The
equation is: √
Equations used in studying an alternating X sinusoidal oscillogram are:
- The maximum voltage: y X - The effective voltage: √ - The period (time needed by one signal X to be complete):
- Frequency:
2-3- House Electricity: Our houses are fed, from the EDL, by an alternating sinusoidal voltage whose effective value is 220V and of frequency 50Hz. All domestic appliances are connected in parallel for independent functioning. Any house is equipped with an electric meter that measures the amount of electric energy consumed by the habitation; and a circuit breaker that protects the house against excess current.
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Grade 9: Electricity Summary
3- Resistors Resistor: An electric appliance that converts electric energy into thermal energy (heat). It is used to heat, to protect, or to regulate electricity. Resistance: The rate of voltage, across the terminals of a device, to the electric
current flowing though it: . Its SI unit is the Ohm (Ω).
2-4- Measuring resistance: Use the ohmmeter (an application of the multimeter (R) also) which should be connected in parallel across the object with no voltage source. (Ω)
2-5- Ohm’s law for a resistor:
In a resistor, the voltage across its terminals and U (V) the current flowing through it are proportional. Its
resistance is, thus, constant: U(V) = R(Ω) x I(A). 5 The characteristic voltage-current of a resistor is a straight line passing through the origin. Graphically, the resistance is the slope of this 2 1 line: I
0 0.2 0.5 (A) 2-6- Grouping resistors: A group of resistors can always be replaced by one resistor whose resistance is equivalent to all of them. The equivalent resistor can be treated as a simple resistor.
In series:
In parallel:
In case of two resistors in parallel, a shortcut can be used:
4- Electric power and Safety: 4-1- Electric power: Mathematically, electric power is the product of voltage and current intensity: P(Watts) = U(V) x I(A). In a resistor where U = R x I, the electric power can also be written as:
or
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Grade 9: Electricity Summary
4-2- Electric energy:
Electric energy is given by .
An alternative set of units can also be used: Where 1kW = 1000 W
1h = 3,600s
In a resistor where , electric energy can be calculated by: This energy is liberated as thermal energy and it is known as Joule’s effect.
4-3- Electric safety: The dangers of electricity are: electrocution and fire which result of excess electric current. 1- To protect an appliance against fire and excess current, a fuse or a circuit breaker can be used. A fuse (figure 4-3-a) is connected on the live wire and it melts down if the current flowing through it exceeds its rated value.
Figure 4-3-a
A circuit breaker (figure 4-3-b) is also connected to the live wire and it is released if current flowing through it exceeds its rated value.
Figure 4-3-b
2- To protect users (people) against electrocution and leaking current a differential circuit breaker or grounding are used. A differential circuit breaker (figure 4-3-c) is connected on both, live and neutral wire and it measures the difference in currents flowing in these two lines. Once the difference exceeds a certain value the breaker is released. Figure 4-3-c
Grounding (fig. 4-3-d) is a process in which “ground” is used to dispose any leak of current if it happens and thus prevent it from flowing through users.
Figure 4-3-d
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Grade 9: Electricity Summary
Sample Problems
Exercise 1: Grouping Resistors
Consider the following circuit where the resistances of the given resistors are: R1 = 30 Ω, R2 = 60 Ω, R3 = 10 Ω, and R4 = 20 Ω. The voltage across the terminals of the dry cell is UPN = 24V.
1- Calculate the resistance RAD of the resistor across A and D. 2- Calculate the resistance RAB of the resistor equivalent to the connection between points “A” and “B”.
3- Verify that UAB = 24V. 4- Determine the current delivered by the generator.
5- Calculate the voltage across AD: UAD. 6- Giving all the necessary explanations, determine the currents I1 and I2 flowing in (R1) and (R2) respectively.
Exercise 2: Resistors and Resistance
During a lab session, grade 9 students were distributed over (1) (6) two groups: A and B. The aim of the session is to verify whether a load (D) is a resistor or not and calculate its resistance. A (2) A- Resistance: Load (5) Group A connected the circuit represented in the adjacent figure. (V) 1- Label each of its 6 elements. ( Don’t redraw) (4) 2- This group did some measurements and recorded the results. (3) I (A) 0 0.4 0.7 0.9 1.2 U (V) 0 4 7 9 12
Trace the graph showing the variation of voltage (U) as a function of current intensity (I). 3- The group concluded directly that the studied device is a resistor. a- Justify their conclusion giving the necessary explanation. b- Deduce that the resistance of (D) is R = 10Ω. B- Verification: To assure their classmates results, group B used a device that measures resistance directly. 1- Name this device. 2- Draw a figure showing how is it connected with (D) to measure its resistance.
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Grade 9: Electricity Summary
Exercise 3: Measurement Instruments
The given diagram represents an electric circuit of an electric motor, lamp, dry cell that provides a constant voltage 12V, a switch and connecting wires.
First case: the switch K is open 1- How are the lamp and the motor connected (in series or in parallel)? 2- Determine the voltage across the terminals of the switch, lamp and the motor. 3- What is the value of the electric current in the circuit?
Second case: the switch K is closed, UBC = 7V and the current sent by the cell is 100mA.
1- Find UPD, UDA and UAB. 2- Find the current carried by the lamp and the motor.
3- Draw the circuit again and show the connection of a voltmeter that measures UCB showing its COM terminal. What would be the reading of the voltmeter? Justify. 4- On the same diagram, show the connection of an ammeter to measure the current in the circuit when it indicates positive reading.
5- An oscilloscope is connected to measure the voltage UBA where its vertical amplitude gain is adjusted to 2 V/div. What is the value of the voltage measured by the oscilloscope?
6- Find the number of division displaced by the luminous line. 7- Show the connection of the oscilloscope on the same diagram. 8- A connecting wire is added between points A and B. a- What is the value of each of the voltages of the lamp and the motor? b- Is there any risk on the motor? Explain.
Exercise 4: Using the Oscilloscope
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Grade 9: Electricity Summary
The figure above represents an oscilloscope branched across a generator (the connections of the generator are not represented).
1- Determine, from the figure : a- The values of the vertical and the horizontal sensitivities of the oscilloscope. b- The mode of functioning of the oscilloscope. c- The nature of the voltage delivered by the generator.
2- The oscilloscope displays the voltage UAB. Show the connection of the oscilloscope terminals on a figure on your answer sheet. 3- What are the maximum value and the period of the voltage of the generator? 4- Can the effective value be calculated? Why? 5- What do you observe if a vertical sensitivity of is chosen? Justify.
Exercise 5: AC Voltage
The aim of this exercise is to study the functioning of a lamp (G) when connected to an AC generator. In the adjacent figure (figure a), you are given the following: (L)
- A generator (G). Y - A lamp with the inscriptions (6V, 0.5A).
- An oscilloscope with a vertical sensitivity Sv = 3V/div and time base Sh = 5 ms/div. The screen of the oscilloscope displays the oscillogram shown in figure b. 1- Precise the type of the alternating voltage used. 2- Calculate its period and deduce its frequency. 3- Calculate its maximum voltage. 4- The oscilloscope is replaced by a voltmeter which reads 5.2 V. What does this voltage represent? 5- Does this lamp function normally? Why? 6- We turn off the sweeping. What will the shape of the
displayed voltage UCD be?
7- Upon changing one of the two sensitivities, the oscillograms of figure c is obtained. Which sensitivity is changed and what is its new value.
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Grade 9: Electricity Summary
Exercise 6: House Electricity
The installation of a house is equipped with a circuit breaker of 30A. The following appliances are connected across this installation:
- A heater that needs an electric current of intensity 12.5A to function normally. - An iron of rated power 1320Watts. - A washing machine that uses 7A. - 4 eco-lamps of 55W each. - A toaster of nominal current 3A. 1- These appliances are connected in parallel, why? 2- Give the characteristics of the electricity at our houses. 3- Consider the iron. a- Calculate the electric current flowing through the iron during normal functioning. b- Find a relation between voltage, resistance and power; and then deduce the value of the resistance of the iron. c- Is the use of a 5A-fuse, suitable? How could you tell? 4- Calculate the main current of this installation when all appliances function simultaneously. 5- Is the circuit breaker released? Justify. 6- The circuit breaker does not protect people living in the house. Why? What should be done (or added to the installation) to protect them?
Exercise 7: Cost of a Shower
Elsy’s house is equipped with a water heater is rated by 220V, 1760W. To heat up water from 15oC to 60oC, the heater uses thermal energy of 8.64x106J.
1- The water heater is made of resistors mainly; how can you tell? Explain by stating the law or effect you need. 2- Write the given energy in Ws, and in kWh. 3- How much time does Elsy need to heat up water to take a shower. 4- Knowing that 1kWh costs around 120L.L. How much would this shower cost?
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