Tiêu đề Theory.pdf ✅

  Digital Pvt. Ltd. [1] Alternating Quantity An alternating quantity (current  or voltage V) is one whose magnitude changes continuously with time between zero and a maximum value and whose direction reverses periodically. Comparison of AC and DC Alternating Current AC Direct Current DC Can be Generated by using AC Generator. Can be Generated by using DC Generator, Battery, solar panels. Inverter converts AC into DC. Rectifier converts AC into DC. Can be controlled using Transformer. Cannot be controlled using Transformer. Types of current Examples of AC : (1) (2) (3) (4) i = i0sint O + T/2 – T t Changes direction periodically i0 t Flows only in one direction O i t i0 –i0 Sinusoidal AC i t i0 –i0 Square AC i t i0 –i0 Triangular AC i t i0 –i0 Saw-tooth AC Introduction Part -01 TG: @Chalnaayaaar
  Digital Pvt. Ltd. [2] Alternating Current – Part-01 Equation for I and V Alternating current or voltage varying as sine function can be written as I = I0 sin t or I = I0 cos t where I = Instantaneous value of current at time t, I0 = Amplitude or peak value Standard definitions 1. Amplitude of AC : The maximum value of current in either direction is called peak value or the amplitude of current. It is represented by 0 2. Time Period : The time taken by alternating current to complete one cycle of variation is called periodic time or time period of the current. 3. Frequency : The number of cycle completed by an alternating current in one second is called the frequency of the current. UNIT : (cycle/s) or (Hz) In India : f = 50 Hz , supply voltage = 220 volt In USA : f = 60 Hz , supply voltage = 110 volt t 0 –I0  T 4 T 2 3 4 T  as a sine function of t t 0 –0  T 4 T 2 3 4 T  as a cosine function of t T TG: @Chalnaayaaar
  Digital Pvt. Ltd. [1] Important values of alternating quantities  Instantaneous Values  Peak Values  Average Values  Root Mean Square (RMS) Values Instantaneous Values The instantaneous value is “the value of an alternating quantity at a particular instant of time in the cycle” Illustration 1. Find out instantaneous current value for I = I0 sint at T t 8 = Solution. As I = I0 sint At T t 8 = 0 0 2 T I I sin I sin T 8 4      = =       0 I I 2 = Illustration 2. Find out instantaneous voltage for V = 200 sin (400 t) at 1 t sec 800 = Solution. As V = 200 sin 400 t At 1 t sec 800 = 1 V 200sin 400 800 =   V = 200 volt Instantaneous, Peak and Average Values Part -02 TG: @Chalnaayaaar
  Digital Pvt. Ltd. [2] Alternating Current – Part-02 Illustration 3. Find out instantanous value for 0 I I sin t 6    =  −     at T t 2 = Solution. 0 0 0 2 T I I I sin I sin T 2 6 6 2      =  − = =     Peak values/Maximum value The maximum value of alternating quantity (I or V) is defined as peak value. It may or may not be equal to amplitude. Some common examples: 1.  = 0 sint peak value = 0 Amplitude = 0 2.  = 0 cost peak value = 0 Amplitude = 0 3.  = 0 sin(t+) peak value = 0 Amplitude = 0 4.  = 1 + 0 sint peak value =1+0 Amplitude = 0 5.  = 1 sint + 2 cost peak value = ( ) 2 2 1 2 I I + Amplitude = 2 2 1 2 I I + 6.  = 1 + 2 sint + 3 cost peak value = 2 2 0 2 3 I I I + + Amplitude = 2 2 2 3 I I + 7.  = 0 sint cost peak value = 0 I 2 Amplitude = 0 I 2 Illustration 4. Find the time taken by the current to reach half of its maximum value. Solution. 0 0 I I sin t 2 =  1 sin t t 2 6   =   = 2 T t t T 6 12    =  = Illustration 5. Find the time taken by current to reach 0 I 2 , if the frequency of current is 50Hz. Solution. At I = 0,  = 0° At 0 I I 2 = , 4  = As T T t 2 4 8   =  =  or 1 1 t 2.5ms 8f 8 50  = = =  TG: @Chalnaayaaar