Slide 1 / 69 Slide 2 / 69 Topics to be covered Sources of alternating EMF Transformers Alternating Current AC Circuits and Impedance LRC Series AC Circuits Resonance in AC Circuit Oscillations Slide 3 / 69 Slide 4 / 69 Sources of Alternating EMF Sources of Alternating EMF A simple generator consists of many coils of wire wound on an armature Faraday's discovery of electro- that can rotate in a magnetic field magnetic induction played a very created by a permanent magnet. The important role in the development of axle is turned by a hand. In real life it the electric generator. A generator can be any mechanical means (falling transforms mechanical energy into water, steam flow, car motor belt...). electrical energy.The generator An EMF is induced in the coil because presented by the diagram to the left of constant change in the magnetic can be found in every high school flux through the coil. The turning coil physics lab. is connected to the external circuit by two slip rings and brushes connected to them. Slide 5 / 69 Slide 6 / 69 Sources of Alternating EMF 1 Which of the following is the unit of the magnetic flux? Now it is time to look at the AC current production in more detail. When a T . m A single loop of wire is placed in a Wb . m uniform magnetic field the magnetic B flux is determine by the following Wb/m 2 C formula: T . m 2 D Where θ is an angle between magnetic field B and the normal to the loop. When the loop rotates the angle changes with time θ = ω t. It proves that the magnetic flux varies with time even when the field stays constant.
Slide 7 / 69 Slide 8 / 69 2 A rectangular loop of wire with a size of 10x20 cm is placed 3 A rectangular loop of wire with a size of 10x20 cm is placed in a uniform magnetic field of 2 T. Find the magnetic flux in a uniform magnetic field of 2 T. Find the magnetic flux through the loop when the angle between the field and the through the loop when the angle between the field and the normal to the loop is 60 o . normal to the loop is 0 o . A 0.05 Wb A 0.05 Wb B 0.02 Wb B 0.02 Wb C 0.01 Wb C 0.01 Wb D 0.04 Wb D 0.04 Wb Slide 9 / 69 Slide 10 / 69 Sources of Alternating EMF 4 The magnetic flux through a coil of wire changes from 0.5 Wb to 2.5 Wb in 0.1 s. What emf is induced in the coil? According to Faraday's Law the A 50 V induced emf is proportional to the rate of change of magnetic flux. B 40 V C 20 V D 10 V The induced emf varies sinusoidally with time. When an external circuit is connected to terminals ab in the diagram above, the electric current caused by the emf is also sinusoidal which we call an alternating current or ac current. Slide 11 / 69 Slide 12 / 69 A square coil of wire with 10 turns and an area of 0.5 m 2 is Sources of Alternating EMF 5 placed in a parallel uniform magnetic field of 0.75 T. The coil is turned so it is now perpendicular to the magnetic field. This action takes 0.15 s to complete. What is the emf induced This equation is valid for any shape loop. When a single in the coil? loop is replaced with a coil consisting of N loops the formula looks slightly different. A 25 V B 20 V Since ω is measured in radians per second (rad/s), we C 15 V can write ω =2 π f, where f is the frequency. D 10 V The United States and Canada use generators operating at the frequency of 60 Hz, although 50 Hz is used in many countries.
Slide 13 / 69 Slide 14 / 69 7 An AC generator has a coil with 10 loops of wire and an area 6 An AC generator consists of 60 loops of wire of area 0.4 of 0.08 m 2 . The coil rotates at a constant rate of 60 rev/s in a m 2 . What is the induced emf generated by the loops if they uniform magnetic field of 0.4 T. What is the maximum rotate at a constant angular velocity of 15 rad/s in an induced emf in the coil? uniform magnetic field of 0.15 T? A 100 V A 90.7 V B 140 v B 100.4 V C 180 v C 110.2 V D 200 v D 120.6 V Slide 15 / 69 Slide 16 / 69 8 An AC generator consists of 200 turns of wire of area 0.25 9 An AC generator consists of 100 turns of wire of area 0.4 m 2 and total resistance of 25 Ω . The generator rotates at a m 2 and total resistance of 30 Ω . The generator rotates at a constant rate of 60 rev/s in a uniform magnetic field of 0.04 constant rate of 60 rev/s in a uniform magnetic field of 0.05 T. Find the maximum induced current. T. Find the maximum induced current. A 10.2 A A 10.2 A B 30.1 A B 20.1 A C 25.7 A C 25.7 A D 44.2 A D 31.4 A Slide 17 / 69 Slide 18 / 69 Sources of Alternating EMF Sources of Alternating EMF It is hard to imagine our life without ac current. It became so popular because of its simple production and, most importantly, its long-distance transmission through electrical lines. With the combination of an ac transformer it is easy to minimize i 2 R energy losses in the cables. These two graphs show the time variation of the magnetic flux through the loop and the resulting EMF at terminals ab. At time t = 0 the angle θ =90 o .
Slide 19 / 69 Slide 20 / 69 Transformers Transformers A transformer consists of two coils of wire known as primary and secondary coils. The A transformer is a device for coils are linked by a soft iron core which is increasing or decreasing an ac laminated to prevent eddy-currents losses. In voltage. Transformer are found the iron core all the magnetic flux produced in everywhere: in TV sets, on utility the primary coil at the same time passes poles, in converters and through the secondary coil. chargers. In our discussion we ignore energy losses in the resistance of the coils and due to eddy- currents. It is a good approximation for real transformers, which provide more than 99% of efficiency. Slide 21 / 69 Slide 22 / 69 Transformers Transformers When an ac voltage is applied to the The ratio between the secondary and primary voltage is called primary coil, the changing magnetic field it the transformer equation: produces will induce an ac voltage of the same frequency in the secondary coil. The magnitude of the secondary voltage depends on the number of turns in each coil. From Faraday's Law the secondary If N s is greater than N p , we have a step-up transformer.The voltage is: secondary voltage is greater than the primary voltage. If N s is less than N p , we have a step-down transformer.The secondary voltage is less than the primary voltage. The input of the primary voltage also depends on the rate of change of flux: Slide 23 / 69 Slide 24 / 69 10 A step-down transformer has 100 turns in the primary coil 11 A step-up transformer is design to increase voltage from and 10 turns in the secondary coil. What is the voltage in 12 V to 120 V. What is the number of turns is in the the secondary coil if 110 V applied to the primary coil? secondary coil if the primary coil has 20 turns? A 11 A 40 B 10 B 100 C 110 C 140 D 100 D 200
Slide 25 / 69 Slide 26 / 69 Transformers 12 A 4 A current flows through a primary coil of a transformer. The primary coil has 50 turns. How many turns must be in A well-designed transformer can have efficiency greater than the secondary coil in order to produce 28 A of current in it? 99%. The power input equals the power output. A 14 B 28 C 32 D 48 When a step-up transformer increases an ac voltage at the same time it decreases an ac current by the same number. When a step-down transformer decreases an ac voltage at the same time it increases an ac current. Slide 27 / 69 Slide 28 / 69 Transformers 13 A transformer has 100 turns in the primary coil and 400 turns in the secondary coil. What is the current in the primary coil if 5 A flows through the secondary coil? A 20 B 15 C 10 D 5 The diagram above demonstrates the importance of step-up and step-down transformers in the transmission of electricity. Slide 29 / 69 Slide 30 / 69 AC Circuits and Impedance 14 An AC current in a circuit with a resistance R is given by In this part of the chapter we will examine, one at a time, how the following formula . If the peak current is 1.41 a resistor, a capacitor, and an inductor behave when A what is the rms current in the circuit? connected to a source of alternating emf. We assume in each case that the emf gives rise to a current: A 5 A B 3 A Where I o is the peak current (maximum value). C 2 A We must know that all ac meters are design to measure I rms D 1 A and V rms (root-mean-square) current and voltage instead of peak current and voltage. The formulas below show the relationships between them.
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