LECTURE -6

• DC voltages and Currents are independent of time (apart from any transient state)
• In DC circuits, current and voltage were in phase, i.e. the current followed voltages without any delay as the impedance is a pure resistance

  
• AC Voltage and Current waveforms

  Time dependTime-dependentent, magnitude varies with time, phase difference introduced between current and voltage due to aACc impedance
• AC Stands for


  Alternating Current
• AC waveform


  Rises from zero to a positive maximum value, returns to zero, goes to a negative maximum value, returns to zero, and the whole process repeats as time progresses
• Sine wave


  A signal which has the form of a sine or cosine function
• Voltage generated by all commercial utilities around the world is sinusoidal
• Peak value


  Absolute value of the greatest positive magnitude existing with the sine wave quantity
• Positive and negative values of a pure sine wave voltage are equal in magnitude
• Peak-to-peak value


  Sum of the positive and absolute negative peak values
• For a pure sine wave, the peak-to-peak value is 2 x the peak value
• Effective value (RMS value)

  Value that would cause the same heating effect as a DC voltage of the same value
• The effective value is 0.707 of the peak value
• If a DC voltage across a resistor caused it to heat at a certain rate

  An AC voltage of the same effective value would cause it to heat at the same rate
• Cycle


  A complete occurrence of events, when a sine wave value completes 360 degrees
• Types of AC waveforms:

  sinusoidal, square wave, Triangular wave

  
• Sinusoidal voltage source


  Generates a voltage that varies sinusoidally with time
• t


  Time (s)
• Vm


  Maximal amplitude of the sinusoidal voltage (V)

  
• T


  Period of the function (s)
• f


  Frequency of the sine function (s-1 or Hz)
• w


  Angular frequency (radians/second)
• Ф


  the phase angle (radians).
• The faster a cycle occurs the higher its frequency.
• Faster means less time in seconds.
• Frequency ( f ) is the inverse of the period of the cycle.
• Frequency is stated in (HERTZ) Hz.
• The PERIOD of the cycle is T.
• The period “T” of a periodic waveform


  the time required for one complete cycle or number of seconds per cycle.
• The equation of a voltage sine wave is given by:


  v(t) =Vmax Sinwt
• wt


  the argument of the wave.
• phase shift

  
• • In DC circuits, the impedance was simply resistance and was independent of frequency.
• • In AC circuits, the impedance is complex and composed of resistance R, inductance L, and capacitance C.
• For frequencies up to a few hundred kHz, resistance for all practical purposes is independent of frequency.
• The voltage across an inductor is the inductance, L multiplied by the derivative of the current.
• Inductive Reactance is a perfect inductor has no electrical resistance.
• L 


  Inductance in Henry
• Inductive Reactance


  𝑋𝐿 = 2𝜋𝑓𝐿 = ω𝐿 ohm
• The equivalent inductance of N series-connected inductors is the sum of the individual inductances