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# Et201 chapter1 ac voltage

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### Et201 chapter1 ac voltage

1. 1. TOPIC 1 : ALTERNATING VOLTAGE AND CURRENTA) DC and AC • Direct current (DC) is current that flows in one direction only. DC voltage has a fixed polarity. o For example, +12V a DC represents 12 volts in the positive direction, or -5V DC represents 5 volts in the negative direction. • A DC voltage source is a voltage source that produces direct current. o Examples: Batteries , dc power supplies (such as the power supply built into the trainer that you use in lab) DC generators , fuel cells and solar cells are DC voltage sources • Alternating current (AC) is current whose direction periodically reverses. o An AC voltage source is a voltage source that produces alternating current. AC voltage switches polarity back and forth. o The direction alternates between 50 and 60 times per second, depending on the electrical system of the country. o Examples: Electrical outlets in the walls of your home provide alternating current. The trainer that you use in lab also contains an AC voltage source called a function generator.Waveform • In DC circuits, current and voltage remain constant as time passes. Voltage (v) • V Time (μsec) t V Time(μs) • But in AC circuits the voltage and current change as time passes. • Graph of a current or voltage versus time is called a waveform. Below are several examples of AC voltage waveforms. because the voltage changes polarity Voltage (v) Time(μs)shs/ppd/dis2010 1/15
2. 2. Voltage (v) Time (μs) Voltage(mv) Time(ms) Advantages of AC over DC: • The alternating current is the current which can travel with a large distances without being a large loss in energy while the direct current cannot travel through the long distances without any loss. DC power degrades as it moves away from its generating source; the further away, the less power. • AC voltages can be readily transformed to higher or lower voltage levels, by a transformer With direct current it is not possible to use a transformer to change voltage. • greater reliability and efficiency • lower cost of manufacture • Tuning circuits : AC electricity also allows for the use of a capacitor and inductor within an electrical or electronic circuit. A combination of a capacitor, inductor and resistor is used as a tuner in radios and televisions. Without those devices, tuning to different stations would be very difficult.B) Faradays Law• Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil.• No matter how the change is produced, the voltage will be generated.• The change could be produced by : o changing the magnetic field strength, o moving a magnet toward or away from the coil, o moving the coil into or out of the magnetic field, o rotating the coil relative to the magnet• In the Electromagnetic Induction, when a single wire conductor moves through a permanent magnetic field thereby cutting its lines of flux, an EMF is induced in it.• However, if the conductor moves in parallel with the magnetic field in the case of points A and B, no lines of flux are cut and no EMF is induced into the conductor,• but if the conductor moves at right angles to the magnetic field as in the case of points C and D, the maximum amount of magnetic flux is cut producing the maximum amount of induced EMF.• Also, as the conductor cuts the magnetic field at different angles between points A and C, 0 and 90o the amount of induced EMF will lie somewhere between this zero and maximum value.• Then the amount of emf induced within a conductor depends on: o the angle between the conductor and o the magnetic flux as well asshs/ppd/dis2010 2/15
3. 3. o the strength of the magnetic field. N C B A D SBasic Single Coil AC Generator• As the coil rotates anticlockwise around the central axis which is perpendicular to the magnetic field, the wire loop cuts the lines of force set up between the north and south poles at different angles as the loop rotates.• The amount of induced EMF in the loop at any instant of time is proportional to the angle of rotation of the wire loop.• As the loop rotates, electrons in the wire loop flow in one direction around the loop. When the wire loop moves across the magnetic lines of force in the opposite direction, the electrons in the wire loop flow in the opposite direction. Then the direction of the electron movement determines the polarity of the induced voltage.• When the loop or coil rotates one complete revolution, or 360o, one full sinusoidal waveform is produced with one cycle of the waveform being produced for each revolution of the coil. As the coil rotates within the magnetic field, the electrical connections are made to the coil by means of carbon brushes and slip-rings which are used to transfer the electrical current induced in the coil.• The amount of EMF induced into a coil cutting the magnetic lines of force is determined by the following three factors. o Speed - the speed at which the coil rotates inside the magnetic field. o Strength - the strength of the magnetic field o Length - the length of the coil or conductor passing through the magnetic field• The frequency of a supply is the number of times a cycle appears in one second and that frequency is measured in Hertz. As one cycle of induced emf is produced each full revolution of the coil through a magnetic field comprising of a north and south pole as shown above,.• So by increasing the speed of rotation of the coil the frequency will also be increased.• Therefore, frequency is proportional to the speed of rotation, ( ƒ Ν ) where Ν = r.p.m.shs/ppd/dis2010 3/15
4. 4. Displacement of a Coil within a Magnetic Field 1 cycle +Vm emax einst θ=ωt ω -Vm Instantaneous Value .C) Instantaneous Voltage• The instantaneous values of a sinusoidal waveform = Maximum value x sin θ Vi = Vmax x sin θ o Where, Vmax is the maximum voltage induced in the coil o and θ = ωt, is the angle of coil rotation.• The instantaneous value of the waveform and also its direction will vary according to the position of the coil within the magnetic field.• The waveform studied most frequently in electrical circuit theory is the sine wave.• a sine wave must pass through the origin (the point where the x-axis crosses the y-axis).Sinusoidal• The more general term sinusoid is used to describe any waveform that has the same shape as a sine wave but that may be shifted to the right or to the left along the x-axis. It does not pass through the origin:shs/ppd/dis2010 4/15
5. 5. Periodic Waveform• A periodic waveform is a waveform whose values are repeated at regular intervals.• All of the waveforms shown above are periodic waveforms.Waveform Parameters• Important parameters associated with periodic waveforms include: o Period o Frequency o Peak Value o Peak-to-Peak Value o RMS Value (also called effective value) o Average Value• Each of these terms is explained below.• The plot of a periodic waveform shows a regularly repeating pattern of values, each of which is called a cycle. Vp Vp-p I cyclePeriod• The period of a waveform is the time required for completing one full cycle.• The symbol for period is T.• Period is measured in units of seconds, abbreviated s.• Example: The sine wave shown above has a period T of 50 ms.Frequency• The frequency of a waveform is the number of cycles that is completed one second• The symbol for frequency is f• Frequency is measured in units of cycles per second, or Hertz, abbreviated Hz. f=1/T and T=1/fPeak Value• Peak voltage is the voltage measured from the baseline of an ac waveform to its maximum, or peak, level.• Unit: Volts peak (Vp)shs/ppd/dis2010 5/15
6. 6. • Symbol: Vp• The peak value of a waveform is also called amplitude,Peak-to-Peak Value• Peak-to-peak voltage is the voltage measured from the maximum positive level to the maximum negative level.• Unit: Volts peak-to-peak (Vp-p)• Symbol: Vp-pRMS Value (or Effective Value)• RMS voltage is the amount of voltage that is required for producing the same amount of heat as you would get if you connected a DC source across that same resistor.• Unit: Volts (V)• Symbol: Vrms• The RMS voltage of a sinusoidal waveform is equal to 0.707 times its peak value. Vrms = 0.707 Vp• A multimeter set to AC mode measures rms valuesAverage Value• The average value of a waveform is the average of its values over a time period.• Any waveform that is symmetrical about the time axis has zero average value over a complete cycle.• Sometimes, though, its useful to refer to the waveforms average value over a half cycle.• sine waves average value over a half ccyle is equal to 0.636 times its peak value.• The average value of a waveform is also called its DC value. Vave = 0.637 VpInstantaneous Value• The instantaneous value of an ac waveform is its value at a specific instant of time. You can use the mathematical expression for a waveform to find the waveforms instantaneous values at specific times.• Example: The instantaneous value of 10 V sin(377t) at time 3 s is equal to 266 mV, v = 10 x sin(377 x 3) = 266 mV• Since ω is in rad/s, your calculator must be in Radians mode when you do this calculation.Form Factor and Crest Factor• Form Factor and Crest Factor can be used to give information about the actual shape of the AC waveform.• Form Factor is the ratio between RMS value and the average value is given as. Form Factor = R.M.S value = 0.707 x Vmax = 1.11 Average Value 0.637 x vmax• Crest Factor is the ratio between the R.M.S. value and the Peak value of the waveform and is given as.shs/ppd/dis2010 6/15
7. 7. Crest Factor (Peak Factor) = Peak Value = Vmax = 1.414 R.M.S Value 0.707 x VmaxExample1. A sinusoidal alternating current of 6 amps is flowing through a resistance of 40Ω. Calculate the average voltage and the peak voltage of the supply.Answer: The R.M.S. Voltage value is calculated as: Vrms = I x R = 6 x 40 =240 V. The Average Voltage value is calculated as: Form Factor = Vrms Vaverage Vavg = Vrms = 240 = 216.2V Form Factor 1.11 The Peak Voltage value is calculated as: Vp = Vrms x 1.414 = 240 x 1.414 = 339.4 volt 2. Two series resistors are connected to an ac source. If there are 7.5 V rms across one resistor and 4.2 V rms across the other, the peak source voltage is 3. If the rms voltage drop across a 15 k resistor is 16 V, the peak current through the resistor is 4. One sine wave has a positive-going zero crossing at 15° and another sine wave has a positive-going zero crossing at 55°. The phase angle between the two waveforms is 5. What is the angular frequency of a waveform whose period is 6.77 µs? : shs/ppd/dis2010 7/15
8. 8. D) Phase of a Sine WaveVoltage (mV) Time (ms) • The pictures of sinusoidal waveforms shown above had voltage on the vertical axis and time on the horizontal axis. • Another way of plotting a sine wave is voltage on the vertical axis, and degrees of the rotors rotation on the horizontal axis. One complete cycle of the sine wave corresponds to 360°. Voltage (Volts) Phase (degrees) v = 300 V sin(θ) • The quantity on the horizontal axis is called the phase of the sine wave. This sine wave has a voltage of 0 V when its phase is 0°, and a voltage of 300 V when its phase is 90°, Radians The Radian, (rad) is defined as a quadrant of a circle where the distance subtended on the circumference equals the radius (r) of the circle. 2∏ rad = 360° 1 rad = 57.5° shs/ppd/dis2010 8/15