Unit 7. Electricity and magnetism

Transcription

1 Unit 7. Electricity and magnetism Index 1.-Electrification: Coulomb s law Electric field vs Magnetic field...5 Types of magnets:...6 Some uses of magnets: Electric circuits...7 Basic Properties of Electric Circuits Ohms Law...9 Ohms Law Relationship Connecting resistors Resistors in series...10 Current Resistors in parallel Mixed circuits Power...14 Practice exam...15 Page 1 of 16

2 1.-Electrification: It is the phenomenon whereby objects acquire an electric charge. The number of protons in an atom equals the number of electrons; therefore atoms are neutral. However, atoms may gain or lose electrons, thereby getting an electric charge. An object is charged positively if the atom has lost electrons. An object is charged negatively if the atom has gained electrons. How is electric charge measured? Coulombs (C). Remember: Other submultiples used: 1.1 Methods of electrification: - By friction. - By induction. - By contact. 1.2 Conducting and insulating materials. Activities: 1 e - has a charge of C 1 mc = 10-3 C (milicoulomb) 1 μc = 10-6 C (microcoulomb) 1 nc = 10-9 C (nanocoulomb) 1 pc = C (picocoulomb) - Conductors: they allow the electric charges to move freely through them, e.g. copper. - Insulators: they do not allow free flow of charges inside them. e.g wood 1.- When an object loses e -, how is its charge? 2.- Say by which methods are objects electrified in the following experiences: a) We rub a glass rod with a silk scarf. b) We approach an electrified glass rod to a neutral ball. c) We touch a neutral ball with an electrified rod. d) You comb your dry hair with a plastic comb. e) You now approach the comb to a trickle of water running from the tap. 3.- Cables of electric supply are lined with plastic. Why? 4.- When rubbing a plastic sheet with a woolen garment, the sheet acquires a 0. 5 pc charge. How many e - in excess does the sheet have? Sol: Page 2 of 16

3 5.- How many electrons lacks an object with a charge of +2.5 nc? 6.- How many e - has in excess an object with a charge of -3 μc? 7.- What charge has an object that has electrons in excess? 8.- What charge has an object that has electrons below? Sol: Sol: Sol: C Sol: C 2- Coulomb s law It was discovered by Priestley in 1766, and rediscovered by Cavendish few years later, but it was Coulomb in 1785 who submitted it to experimental testing. Coulomb s law states that the magnitude of the Electrostatics force of interaction between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distances between them, and has the direction of the line connecting them. The force is repulsive if the charges have the same sign, and attractive if they have different sign. Concerning Coulomb s law it is important to state the following: 1- Point charge means an electric charge located on a geometrical point in space. Obviously, such point charge does not really exist, it is an idealized concept, but it serves as a good approach when we study interaction between electrically charged bodies whose dimensions are very small compared with the distance between them. 2- When we speak of the force between electric charges we always assume that they are at rest (hence the term Electrostatics); It is to be noted that electrical force is a vector quantity- it has magnitude, direction and sense. In mathematical terms, this law refers to magnitude F of the force which each of the two point charges q 1 and q 2 exert on each other separated by a distance r and is expressed as an equation as: Page 3 of 16

4 K being a constant known as Coulomb s constant and the bars meaning absolute value (we work without a sign). The value of K in vacuum is N m 2 /C 2 Units: Force is expressed in Newtons (N). Charges in coulombs (C) Distance in meters.(m) F is the force vector for the electric charges. It can be attractive or repulsive, depending on the sign that appears (signaling whether the charges are positive or negative). Activities: 9- Two electrically charged particles are placed at a distance of 4 mm between them; the magnitude of the electric charges being q 1 = 6 μc and q 2 = -12,0 μc. What is the magnitude of the electrical force exerted on each electric charge? Draw a scheme with the forces. Sol: a) N 10- Determine the force acting on the following electric charges q 1 = C and q 2 = C. Which are at rest and in vacuum at a distance of 5 cm. Will it be attractive or repulsive? Draw a scheme with the forces. Sol: 72 N 11- Determine the distance between two charges, q 1 = -1, C. and q 2 = C. Which are at rest and in vacuum if they attract each other with a force of N. Sol: 0.1 m 12- Two equal electric charges located at a distance of 2 m repel one another in vacuum with a force of N. Calculate the value of the electric charges. Sol: 2 μc 13- A charge of +12 μc attracts another charge with a force of 0.25 N when they are in vacuum at 20 cm of distance. What is the value of the other charge? What is its sign? Sol: C; negative Page 4 of 16

5 14- A charge of +850 nc repels another charge of +425 nc with a force of N. Calculate the distance between them assuming they are both in vacuum. Sol m 15- Calculate the force with which two charges of 5mC and -3mC attract each other if they are in vacuum at a distance of 2 m. Sol: N 16- Work out the value of two equal charges if we know they repel each other with a force of 10-5 N when they are at a distance of 3m. Sol: 10-7 C 17- How far must we place two charges of + 50 μc and -125 μc so that they attract each other with a force of 1N? Sol. 7.5 m 18- Two equal charges repel each other with a force of 10 N when they are placed at a distance of 1cm. Calculate the value of these charges. 3. Electric field vs Magnetic field. Sol: C Electric charge in bodies alters the space surrounding them. The charge creates an electric field. These are the lines that represent the electric field. But exists another type of field, magnetic field that is created by a magnet. A magnet is an object made of certain materials which creates a magnetic field. Every magnet has at least one north pole and one south pole. By convention, we say that the magnetic field lines leave the North end of a magnet and enter the South end of a magnet. Page 5 of 16

6 This is an example of a magnetic dipole ("di" means two, thus two poles). If you take a bar magnet and break it into two pieces, each piece will again have a North pole and a South pole. If you take one of those pieces and break it into two, each of the smaller pieces will have a North pole and a South pole. No matter how small the pieces of the magnet become, each piece will have a North pole and a South pole. It has not been shown to be possible to end up with a single North pole or a single South pole which is a monopole ("mono" means one or single, thus one pole) By the end of the 18th century, scientists had noticed many electrical phenomena and many magnetic phenomena, but most believed that these were distinct forces. Then in July 1820, Danish natural philosopher Hans Christian Oersted published a pamphlet that showed clearly that they were in fact closely related. During a lecture demonstration, on April 21, 1820, while setting up his apparatus, Oersted noticed that when he turned on an electric current by connecting the wire to both ends of the battery, a compass needle held nearby deflected away from magnetic north, where it normally pointed. This was the one and only conclusion: So charge in motion creates magnetism Magnets but also electric current creates magnetic field. Types of magnets: 1. A permanent magnet is an object made from a material that is magnetized and creates its own persistent magnetic field. An everyday example is a refrigerator magnet used to hold notes on a refrigerator door. Materials that can be magnetized, which are Page 6 of 16

7 also the ones that are strongly attracted to a magnet, are called ferromagnetic. These include iron, nickel, cobalt. 2. An electromagnet is made from a coil of wire that acts as a magnet when an electric current passes through it but stops being a magnet when the current stops. So electric charges in motion create magnetic field. Is it possible the opposite? When Michael Faraday made his discovery of electromagnetic induction in 1831, he hypothesized that a changing magnetic field is necessary to induce a current in a nearby circuit. To test his hypothesis he made a coil by wrapping a paper cylinder with wire. He connected the coil to a galvanometer, and then moved a magnet back and forth inside the cylinder. This was the one and only conclusion: Some uses of magnets: So a magnet in motion creates electric current 1. They are used to construct the electrical motors and the generators which convert the electrical energy into mechanical energy and vice verse. 2. They are also used in the speakers which can convert the electrical energy into sound energy. 3. They are used in the electrical bells. 4. They are used in the Maglev trains. In the Maglev trains, the super conducting magnets are used on the tracks on which the train floats. These types of the trains are working on the repulsion force of the magnets. 5. They are also used to sort out the magnetic and non magnetic substances from the scrap(chatarra) 6. They are used in TV screens, computer screens, telephones and in tape recorders. 7. They are used in the refrigerators to keep the door close. 8. The compass which is used to find the geographical directions. 4. Electric circuits Magnitudes in electric circuits: 1. Charge (unit: coulomb, C; letter symbol: q or Q ) The electric charge is the most basic quantity in electrical engineering, and arises from the atomic particles of which matter is made. 2. Potential Difference (unit: volt, V; letter symbol: V ) The potential difference, also known as voltage, is the energy required to move a unit positive charge from one point to another across a circuit element. Page 7 of 16

8 3. Current (unit: ampere, A; letter symbol: I) The electric current is the rate of charge flow in a circuit. I = Q/t 4. Power (unit: watt, W; letter symbol: P ) The electric power is the rate of change of energy. P = W/tCircuits are collections of circuit elements and wires. Wires are designated on a schematic as being straight lines. An electronic circuit is composed of individual electronic components, such as resistors, connected by conductive wires through which electric current can flow. So it is necessary a source of energy like batteries. Basic Properties of Electric Circuits A circuit is always a closed path. A circuit always contain an energy source which acts as source of electrons. In an electric circuit flow of electrons takes place from negative terminal to positive terminal. Direction of flow of conventional current is from positive to negative terminal. An electrical circuit is an interconnection of electrical circuit elements. These circuit elements can be categorized into two types, namely active elements and passive elements. Passive Circuit Elements The most basic of the passive circuit elements is the resistance. They consume energy (i.e. convert from electrical form to a non-electrical form such as heat or light). Resistance (unit: ohm, Ω; letter symbol: R ) The common circuit symbols for the Resistor are shown in figure 1. First figure is the common symbol used for the general resistor, especially when hand-written. Second figure is the most general symbol for the resistor, especially when in printed form. Page 8 of 16

9 5. Ohms Law The relationship between Voltage, Current and Resistance in any electrical circuit was firstly discovered by the German physicist Georg Ohm. Ohm found that, at a constant temperature, the electrical current flowing through a fixed linear resistance is directly proportional to the voltage applied across it, and also inversely proportional to the resistance. This relationship between the Voltage, Current and Resistance forms the basis of Ohms Law and is shown below. Ohms Law Relationship V = Voltage (volts) (V) I = Current (amperes) (A) R = Resistance (ohms) (Ω) V= I R By knowing any two values of the Voltage, Current or Resistance quantities we can use Ohms Law to find the third missing value. Ohms Law is used extensively in electronics formulas and calculations so it is very important to understand and accurately remember these formulas. To find the Voltage, (V) [V=I R] To find the Current, (I) I = V/R To find the Resistance, (R) R = V/I Activities: 19. What is the value of this resistor, in ohms (Ω)? sol: 2700 Ω Page 9 of 16

10 20. An automobile headlight has an average resistance of 24 ohms. Car batteries provide a potential difference of 12 volts. What amount of current passes through the headlight? Sol: 0.5 A 21. An electric heater draws 3.5 A from a 110 V source. What is the resistance of the heating element? Sol: 31.4 Ω 22. If 750 µa is flowing through 11 kω of resistance, what is the voltage drop across the resistor? Sol V 23. A resistance of 10 Ω is placed across a 9 V battery. What current flows through the battery? Sol. I = 0.9 A 6. Connecting resistors 6.1 Resistors in series Current Resistance I = I 1 = I 2 =I 3...etc Voltage V = V 1 +V 2 +V 3...etc 24. A series circuit has 4 resistances of 20, 40, 10 and 5 Ohms. Calculate the Total resistance and the current flowing through each one if the battery has a value of 10 Volts Solutions: Total resistance = 75 Ω. I = 0,13 A Page 10 of 16

11 25. In this circuit, calculate: a ) The total resistance in the circuit b) The current flowing in the circuit. c) The voltage across every resistor Solutions:a) = 40 Ω b) = 0,225 A c ) V1 = 2,25 V2 =1,125 V3 = 5, In the circuit on the left, we have 3 series resistors. We measure 8 volts in the voltmeter ( represented by V ). a) Calculate the voltage across the 20 Ω resistance b) Calculate the equivalent resistor and the current in the battery. sol: V = 32 V; 35 Ω V = 56 V 27. In this circuit, the value of the battery is 1.5 Volts and the current measured in the ammeter is 0.25A. a) Calculate the value of Resistor 2 in this circuit. b) How much current would flow if the value of R was doubled? Solutions: R = 5 Ω and b) I = A Page 11 of 16

12 6.2 Resistors in parallel Resistance Voltage Current I = I 1 +I 2 +I 3...etc 28-5,10 and 25 Ohms resistors are connected in parallel. The value of the battery is 9 Volts Calculate the total resistance and the current flowing through each one Solutions: Rt = 2,94 Ω I 1 = 1,8 A I 2 = 0,9 A and I 3 = 0,36 A 29. What will be the value of the current flowing through the 100 Ohm resistor? And what about the current in the other resistor? Calculate the total resistance of the circuit. Solutions: I 1 = 0,05 A and I 2 = 0,1 A Rt = 33,33 Ω 30. The value of the battery is 12 Volts and the current in the battery 2.1 A. If R 1 = 20 Ω and R 2 = 40 Ω. What is the value of R 3? Sol. 80 Ω Page 12 of 16

13 6.3 Mixed circuits 31. Calculate the equivalent resistor and the current in the battery. 32. Calculate the equivalent resistor and the current in the battery. Sol: Solution: Re = 20 Ω I = 250 ma 33. In the next circuit, calculate the voltage across the 20 Ohm resistor. Re =64,18 Ω I = 77,9mA Page 13 of 16

14 Solution: 1,64 volts 7. Power Power is the measure of how much work can be done in a given amount of time. Mechanical power is commonly measured (in America) in horsepower. Electrical power is almost always measured in watts, and it can be calculated by the formula P = I V Electrical power is a product of both voltage and current, not either one separately. Horsepower and watts are merely two different units for describing the same kind of physical measurement, with 1 horsepower equaling watts. Activities: 34. There are 2 A of current in a circuit that has one 1.5 V battery. What is the electric power consumed by the circuit? Sol: 3W 35. The electric power consumed by a circuit with one light bulb is 3 W. The voltage of the battery is 3 V. What is the current in the circuit? Sol: 1A 36. Determine the amount of electrical energy (in J) used by the following devices when operated for the indicated times. a. Hair dryer (1500 W) - operated for 5 minutes b. Electric space heater (950 W) - operated for 4 hours c. X-Box video game player (180 W) - operated for 2 hours d. 42-inch LCD television (210 W) - operated for 3 hours sol: a. 4.5x10 5 J b. 1.4x10 7 J c. 1.3x10 6 J d. 2.3x10 6 J 37. A hair dryer has a resistance of 100 Ω and it is plugged to a 220 V. If it is operating for 40 minutes, calculate how many kilowatts per hour of energy does it use and how much do you pay if 1kwh = 0,20. Page 14 of 16

15 Practice exam 1. When is a substance positively charged? If a substance has a charge of -2 nc, how many electrons has it gained? If a substance loses e -, how much charge does it have? The electron s charge is C Sol e, C 2. Two charges, the first being +6 μc and the second, -2 μc, are 5 mm apart in vacuum. What is the value of the force between them? Is it repulsive or attractive? Make a graph of the charges and the forces between them. K = N m 2 /C 2 Sol.4320 N 3. Over the course of an 8 hour day, 3.8x10 4 C of charge pass through a typical computer (presuming it is in use the entire time). Determine the current for such a computer. Sol. 1.3 A 4. Defibrillator machines are used to deliver an electric shock to the human heart in order to resuscitate an otherwise non-beating heart. It is estimated that a current as low as 17 ma through the heart is required to resuscitate. Using 100,000 Ω as the overall resistance, determine the output voltage required of a defibrillating device. Sol V 5. Two resistors with resistance values of 6.0 Ω and 8.0 Ω are connected to a 12.0-volt source. Determine the overall current in the circuit if the resistors are a. connected in series. b. connected in parallel. 6. Complete: Page 15 of 16

16 sol. 7. A 541-Watt toaster is connected to a 120-V household outlet. What is the resistance (in ohms) of the toaster? Answer: R = 26.6 Ω 8. Fill the gaps. a) Bar magnets have two poles: and pole. b) The pushing or pulling force of a magnet is strongest of the magnet. c)like poles each other while unlike poles each other. d) Some metallic materials are magnetic and some are not. An example of magnetic is and an example of non magnetic is e) The three methods of electrification are: f) Two charges with sign attract each other. g) The unit of charge in the SI is with the letter h) Coulomb s constant K depends on i) An electrical conductor is An example is j) An electromagnet is Page 16 of 16