# Unit 6 Current Electricity and Circuits

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1 Unit 6 Current Electricity and Circuits 2 Types of Electricity Electricity that in motion. Electricity that in motion. Occurs whenever an moves through a. 2 Types of Current Electricity Electricity that flows in direction. Typical in circuits operating with Electricity that moves at regular intervals. Typically found in. In North America we have operating at In Europe they have operating at. Definition of Electric Current Electric Current is the amount of electrons ( ) that flows through a of a conductor per a certain period of. 1 P a g e

2 Example: Find the amount of current in a wire that has 10.0 C of charge passing through every 2.0 seconds. Page 594 #2. #3 page 594 Direction of Direct Current Consider a simple circuit : Electricity was thought to have traveled from the abundance of electricity ( ) to the deficiency of electricity ( ) This was thanks to 2 P a g e

3 Unfortunately Ben got it wrong. It is actually that flow in a circuit. Electron Flow: Electrons travel away from the, through the circuit, and are attracted towards the. However many university still use flow when talking about the direction flows Electric Potential Recall: and Now we have so Units?? Examples: 1. What is the energy used by a 10.0 Amp lawn mower that operates for 1 hour using 110 Volts? 3 P a g e

4 2. How long would it take a : A) computer monitor operating at 120 V and drawing 0.8 A of current to consume 3.96 MJ of energy? B) heater operating on 240 V drawing 20 A of current? 3. One electron volt (1 ev) is a unit of we will used when dealing with elemental particles in Nuclear Physics. 1 ev is the given to an has its is through a of 1 volt. What is the energy equivalent of 1 ev measured in Joules? Page 621 # P a g e

5 Sources of Electrical Energy: 1. is changed to electrical potential energy in a cell. A chemical reaction that proceeds only one way, where the chemicals gradually become used up is called a If the chemical reaction is, the cell can be recharged and is called a Two or more cells connected together form a of cells, or simply a. Examples A) The Cell ( named after Alessandro Volta) 5 P a g e

6 B) 6 P a g e

7 C) Examples are: These batteries (series of cells) can be by having another source of electrical energy applied to it. This the chemical reaction. 7 P a g e

8 2. This is the source of electricity. If a is moved through a field the electrons in the conductor experience a force which causes them to move resulting in. The energy used to move the conductor is converted into. This energy may be from: 3. : Certain crystals such as and produce electric current if a is exerted on it. Examples are : Also these crystals produce if a electric current is applied to it. An example is a watch. 8 P a g e

9 4. Bi-metal strips of dissimilar metals produce an electric current when the two ends are exposed to different. They are used in : can measure between 0 o C to 275 o C has a range of 0 o C to 1700 o C (can be used for measuring temperature of molten metal.) 5. Converts into electrical energy. It works because electrons of certain materials ( ) absorb energy so that they are able to move away from their atoms, thus producing electric current. Uses: What is the most likely source of electrical energy for each of the following: A) a cellular telephone 9 P a g e

10 B) a digital watch C) a car stereo D) a home DVD player E) a ship to shore radio F) a communications satellite G) a phonograph H) a thermometer used to measure the temperature of hot flue gases 10 P a g e

11 Consider the diagram below. Schematics This is a picture of a. A schematic uses to represent the components of a circuit. It makes circuits much easier to and. Symbols used for schematics are basically with slight variations from text to text. Page 593 contains the symbols that we will use in our electrical circuits Draw the circuit above using these schematic symbols. 11 P a g e

12 What are the energy transformations that occur when the switch is closed? In the the electrons are given potential energy (in a cell this would be due to ). ( ) As the electrons " through the circuit, they give up most of their energy In the the electrons release their energy in the form of. ( ) In the light bulb the energy is given up in the form of: ( ) An insignificant amount of energy is lost due to in the. Also some energy will be lost in the source itself. It is part of the circuit and it does have an. We do NOT usually include these last 2 in any circuit calculations in P a g e

13 NOTE: The light bulb and resistor are called. The cells are called. This is a circuit because there is only one path that can take. In a circuit electrons have a of directions that they can travel The measures current. It is connected in with the light bulb. The that travel through the light bulb must travel through the ammeter. Example: Draw a circuit containing 2 resistors connected in series to a cell. Draw a circuit containing 2 resistors connected in parallel to a cell. 13 P a g e

14 Law of Conservation of Electric Electric charge cannot be or in an electric circuit, nor does it at any point in the circuit. Therefore, the amount of charge approaching a particular point in a circuit must equal the amount of charge that point. The charge can't ". Based on this what could we say about the current in a series circuit? Law of Conservation of Electric As electrons move through an electric circuit they energy in the and energy in the, but the total energy in one trip is equal to the total energy. Therefore a reasonable hypothesis would be How do we determine these drops and rises? with a. are connected in with whatever you are measuring. How could we measure the voltage drop across the load (light bulb)? place a voltmeter in " with the light bulb. Draw the voltmeter on the schematic. 14 P a g e

15 voltage rule: Circuit Analysis "Around any complete through an electric circuit, the of the in electric potential is to the of the in electric potential." Examples: 1. What type of circuit is this? 2 What type of circuit is this? 15 P a g e

16 3. What type of circuit is this? 16 P a g e

17 Draw a schematic diagram of an electrical source and an ammeter connected at a node or junction to two parallel branches, each of which contains a light bulb and an ammeter. What do the arrows on the schematic represent? If A 2 = 1.5 A and A 3 = 2.5 A, what do you think A 1 would read? From the Law of the Conservation of Electric Charge, we can say that the current a junction will equal the current the junction. 17 P a g e

18 Kirchhoff's current rule: At any junction point in an electric circuit the total electric current the junction is equal to the total electric current. I 0 = I 1 + I 2 + I For example: I = o I 0 = I 1 + I 2 + I3 I = 2.5A I = 4.0A I = 6.0A Circuit Guidelines: Example: 18 P a g e

19 Circuit Guidelines: In each part of a circuit, the loads have the same. In each part of a circuit, each load has of the current. In circuits, each load uses of the total potential energy (voltage). In circuits, each load has the same. 19 P a g e

20 Solve the following: 1. Find x P a g e

21 RESISTANCE IN ELECTRIC CIRCUITS Resistors Resistors are, but electrons some of their as they pass through the resistor. Thus resistors are considered to be. Some uses for resistors are: (i) to produce (ii) to produce (iii) to control and ( ) This is to prevent certain circuit components from RESISTANCE IN ELECTRIC CIRCUITS Resistors Consider a simple circuit where a resistor is connected to a battery. Draw this circuit. How do we measure the current in the circuit?. How do we measure the voltage drop in the resistor? Lets vary the voltage and see what happens to the current. 21 P a g e

22 V I What is the slope of this line?? What was the resistance of the resistor? What is the relationship between the resistance and the slope of the Voltage vs Current graph? For a certain resistor, R, the voltage drop across R is to the current passing through R. Thus, 22 P a g e

23 To equate this relation the proportionality constant is the OR which also represents the of the voltage vs current graph. This relationship is called Resistors A resistor is called a because it is fairly independent of the current passing through it. In such cases a graph of V versus I gives a line with slope,. A resistor is because it obeys, where the ratio of is constant. NOTE: There are devices which are not linear. They do not follow Ohm's Law. EX: 23 P a g e

24 An I - V graph for a 30 (ma) Silicon Diode 20 Reverse 10 Forward Bias Bias Knee Voltage Break Down Voltage V (volts) OHM'S LAW The potential difference between any two points in a conductor varies to the current between the two points. R- measured in ( ) V- or measured in volts (V) I - measured in amperes (A) 24 P a g e

25 Problems: V V= 6V V= I=0.25A I= R= R= 80 Page 621 # P a g e

26 ELECTRICAL RESISTANCE (Text 14.5) There are four factors upon which the resistance of an electrical conductor depends: : Resistance is to the length of the conductor. As length, so does the resistance. Example: 1. If you double the length of a conductor, what happens to the resistance? 2. A certain 20 cm long conductor has a resistance of Ω.Find the resistance of the same type of conductor that as a length of 450 km. 26 P a g e

27 2. : Resistance is to the area of the conductor. As area increases by a factor of n, the resistance decreases by a factor of Example: 1. If R = 10. and the area of a conductor increases by a factor of 2 what will be the new resistance? 2. If R = 20., what will the resistance become if the area is changed from : A) 2 cm 2 to 8 cm 2 B) 2 cm 2 to 1 cm 2 C) 2 cm 2 to 0.25 cm 2 Note: The cross sectional area of most conductors are circular. (Why?) 27 P a g e

28 Therefore, we can say that the resistance is inversely proportional to the square of the radius of a circle conductor. (Why?) As the radius increases by a factor of n, the resistance decreases by a factor of Example: If R = 100, find the new resistance if the radius changes from: A) 2 mm to 4 mm B) 2 mm to 6 mm C) 2 mm to 1 mm 3. : As temperature so does the resistance. However some react the opposite way. 4. (Resistivity of material) : The better the material is as a, the resistance it will have. The lower the the the material is at conducting electricity 28 P a g e

29 Resistivities of Common Materials at 20 0 C Type Material m) Conductors Silver 1.5 x 10-8 Copper 1.7 x 10-8 Aluminium 2.6 x 10-8 Tungsten 5.5 x 10-8 Iron 1.0 x 10-7 Platinum 1.0 x 10-7 Nichrome 1.0 x 10-6 Semi-conductors Germanium 0.5 Silicon 2.5 x 10 3 Insulators Glass 1.0 x Rubber 1 x All of these factors can be put into one equation: Where - resistance ( ) - length ( ) - cross sectional area ( ) - resistivity (proportionality constant which changes for different materials and temperatures.) Find the units of. 29 P a g e

30 Questions on resistance 1. A certain piece of copper wire has a resistance of 2.0 x 10-3 ohms. Another piece of copper wire with the same cross-sectional area but twice the length. What is its resistance? 2. A 1.0 m piece of wire with a cross-sectional radius of 3.0 mm has a resistance of 9.0 x 10-4 ohms. If the wire is stretched until its radius is reduced to 1.0 mm, what will be the resistance of a 1.0 m piece? 3. Wire "A" has a length of 2.0 m, a diameter of 2 mm and a resistance of ohms. Wire "B" of the same material has a length of 0.5 m, a diameter of 1 mm. What is the resistance Wire B? 30 P a g e

31 4. A piece of 1.0 m wire has a 3.0 mm radius. If the wire is made from copper, find the resistance of the wire. 5.a) Find the current through a wire that has volts applied to it, if the wire is 400 km long, a radius of 1 cm, and is made from aluminum. b) What is the current if the voltage was volts? Page 604 #2, 3 Page 621 #26, 27, P a g e

32 Consider Finding Total Resistance in Series What can we say about the currents? What about the voltages? To derive an equation for in series, we start with the equation: Divide each term by Since ALL currents are equal in series we can rewrite the above equation as: 32 P a g e

33 Recall Ohm s Law So, and becomes The total resistance, R T, of n resistors connected in series is : Example 1. Find the total resistance NOTE: If there are n resistors ALL of the same resistance, say R, connected in series then 2. Find the total resistance of five 20 resistors connected in series 33 P a g e

34 Finding Total Resistance in Parallel Consider What can we say about the Voltages? What about the Currents? To derive an equation for in parallel, we need to get resistance into the equation: so Rewrite the currents in Since ALL are equal in parallel we can rewrite the above equation as: 34 P a g e

35 Divide each term by The total resistance, R T, of n resistors connected in parallel is : Example 1. Find the total resistance 35 P a g e

36 2. Find the total resistance Note: The total resistance of resistors connected in is always the resistance The total resistance of resistors connected in is always the resistance NOTE: If there are n resistors ALL of the same resistance, say R, connected in then 36 P a g e

37 Example: Find the total resistance of twenty(20) 5 resistors connected in Parallel Series If this was connected to 120V find A) total current If this was connected to 120V find A) total current B) current through each resistor B) current through each resistor Circuit Analysis In more interesting circuits there are of parallel and series branches. Each branch can be replaced by a resistance. Find the current drawn from the 12 V battery if each resistance is 2 37 P a g e

38 Power in Electric Circuits RECALL 2204 Power Formula This is known as UNITS?? What is E in circuit Problems? is the power dissipated by a current through a potential difference Examples: 1. Find the power output by a flashlight bulb drawing 0.3 A from a 1.5 V cell. 2. Find the current drawn by a 500 W resistor when connected to 120 V. 38 P a g e

39 Other Versions of the Power Rule Also from Ohm s Law. Thus becomes: Also from Ohm s Law. Thus becomes: Examples: 1. What is the resistance of a 1500 W hair dryer that draws a current of 13 A? 2. What is the power rating on a light bulb with a resistance of 2, that is connected to 120 V AC? 39 P a g e

40 3. What is the power dissipated through the following resistors at 12 V DC? (a) 15 W (b) 50 W (c) 150 W (d) 300 W Which one would becomes the hottest? Hint: It is the one that has the highest wattage. Which one draws the most current? Page 623 # 36, 37, 38 Consider Power Rules for Series Circuits But, So, And of the currents are 40 P a g e

41 Thus, to find the total power of a series circuit simply ALL of the powers together Consider Power Rules for Parallel Circuits But, So, And of the voltages are Thus, to find the total power of a parallel circuit simply ALL of the powers together. In fact if there is a circuit containing both and branches, you simply of the powers together to find the total power! Examples. 1. Find the total current. 41 P a g e

42 2. Complete the table for circuit below Cost of Electricity Electrical is measured in. Definition: is the dissipated in 1 hour by a load with a power of 1 kw. 42 P a g e

43 Example: 1. If power costs 9.5 /kwh, how much does it cost for a 100 W bulb to light a room for: A) a day B) a year C) 18 years 2. Find the cost of cooking a turkey for 5 hours in an oven that draws 15 A of current from a 240 V supply at a rate of 7.2 / kwh. 43 P a g e

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