Slide 1 / 69 Alternating Current Slide 2 / 69 Topics to be covered Sources of alternating EMF Transformers AC Circuits and Impedance LRC Series AC Circuits Resonance in AC Circuit Oscillations Slide 3 / 69 Sources of Alternating EMF Faraday's discovery of electro- magnetic induction played a very important role in the development of the electric generator. A generator transforms mechanical energy into electrical energy.The generator presented by the diagram to the left can be found in every high school physics lab.
Slide 4 / 69 Sources of Alternating EMF A simple generator consists of many coils of wire wound on an armature that can rotate in a magnetic field created by a permanent magnet. The axle is turned by a hand. In real life it can be any mechanical means (falling water, steam flow, car motor belt...). An EMF is induced in the coil because of constant change in the magnetic flux through the coil. The turning coil is connected to the external circuit by two slip rings and brushes connected to them. Slide 5 / 69 Sources of Alternating EMF Now it is time to look at the AC current production in more detail. When a single loop of wire is placed in a uniform magnetic field the magnetic flux is determine by the following formula: 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 6 / 69 1 Which of the following is the unit of the magnetic flux? T . m A Wb . m B Wb/m 2 C T . m 2 D
Slide 7 / 69 2 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 through the loop when the angle between the field and the normal to the loop is 60 o . A 0.05 Wb B 0.02 Wb C 0.01 Wb D 0.04 Wb Slide 8 / 69 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 through the loop when the angle between the field and the normal to the loop is 0 o . A 0.05 Wb B 0.02 Wb C 0.01 Wb D 0.04 Wb Slide 9 / 69 Sources of Alternating EMF According to Faraday's Law the induced emf is proportional to the rate of change of magnetic flux. 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 10 / 69 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? A 50 V B 40 V C 20 V D 10 V Slide 11 / 69 A square coil of wire with 10 turns and an area of 0.5 m 2 is 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 in the coil? A 25 V B 20 V C 15 V D 10 V Slide 12 / 69 Sources of Alternating EMF This equation is valid for any shape loop. When a single loop is replaced with a coil consisting of N loops the formula looks slightly different. Since ω is measured in radians per second (rad/s), we can write ω =2 π f, where f is the frequency. 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 6 An AC generator consists of 60 loops of wire of area 0.4 m 2 . What is the induced emf generated by the loops if they rotate at a constant angular velocity of 15 rad/s in an uniform magnetic field of 0.15 T? A 100 V B 140 v C 180 v D 200 v Slide 14 / 69 7 An AC generator has a coil with 10 loops of wire and an area of 0.08 m 2 . The coil rotates at a constant rate of 60 rev/s in a uniform magnetic field of 0.4 T. What is the maximum induced emf in the coil? A 90.7 V B 100.4 V C 110.2 V D 120.6 V Slide 15 / 69 8 An AC generator consists of 200 turns of wire of area 0.25 m 2 and total resistance of 25 Ω . The generator rotates at a constant rate of 60 rev/s in a uniform magnetic field of 0.04 T. Find the maximum induced current. A 10.2 A B 30.1 A C 25.7 A D 44.2 A
Slide 16 / 69 9 An AC generator consists of 100 turns of wire of area 0.4 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 0.05 T. Find the maximum induced current. A 10.2 A B 20.1 A C 25.7 A D 31.4 A Slide 17 / 69 Sources of Alternating EMF 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 18 / 69 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.
Slide 19 / 69 Transformers A transformer is a device for increasing or decreasing an ac voltage. Transformer are found everywhere: in TV sets, on utility poles, in converters and chargers. Slide 20 / 69 Transformers A transformer consists of two coils of wire known as primary and secondary coils. The coils are linked by a soft iron core which is laminated to prevent eddy-currents losses. In the iron core all the magnetic flux produced in the primary coil at the same time passes through the secondary coil. 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 Transformers When an ac voltage is applied to the primary coil, the changing magnetic field it 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 voltage is: The input of the primary voltage also depends on the rate of change of flux:
Slide 22 / 69 Transformers The ratio between the secondary and primary voltage is called the transformer equation: If N s is greater than N p , we have a step-up transformer.The 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. Slide 23 / 69 10 A step-down transformer has 100 turns in the primary coil and 10 turns in the secondary coil. What is the voltage in the secondary coil if 110 V applied to the primary coil? A 11 B 10 C 110 D 100 Slide 24 / 69 11 A step-up transformer is design to increase voltage from 12 V to 120 V. What is the number of turns is in the secondary coil if the primary coil has 20 turns? A 40 B 100 C 140 D 200
Slide 25 / 69 Transformers A well-designed transformer can have efficiency greater than 99%. The power input equals the power output. 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 26 / 69 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 the secondary coil in order to produce 28 A of current in it? A 14 B 28 C 32 D 48 Slide 27 / 69 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
Slide 28 / 69 Transformers The diagram above demonstrates the importance of step-up and step-down transformers in the transmission of electricity. Slide 29 / 69 AC Circuits and Impedance In this part of the chapter we will examine, one at a time, how a resistor, a capacitor, and an inductor behave when connected to a source of alternating emf. We assume in each case that the emf gives rise to a current: Where I o is the peak current (maximum value). We must know that all ac meters are design to measure I rms and V rms (root-mean-square) current and voltage instead of peak current and voltage. The formulas below show the relationships between them. Slide 30 / 69 14 An AC current in a circuit with a resistance R is given by the following formula . If the peak current is 1.41 A what is the rms current in the circuit? A 5 A B 3 A C 2 A D 1 A
Slide 31 / 69 15 An AC voltage is applied to a circuit with a total resistance R. What is the rms voltage if the peak voltage is 170 V? A 50 V B 70 V C 120 V D 170 V Slide 32 / 69 AC Circuits and Impedance Resistor When a resistor is connected to an ac source , the current increases and decreases with voltage in phase. They reach maximum and minimum values at the same time. Average power dissipated in the resistor: Slide 33 / 69 A 2000 Ω resistor is connected to an AC circuit with I rms = 16 0.25 A? What is the average power in dissipated in the resistor? A 100 W B 200 W C 400 W D 500 W
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