Electrical Circuits I Lecture 10
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Electric Circuits I “Dr. Ahmed El-Shenawy” <Dr Hadi El-Helw> <Dr Ahmed El-Shenawy> Electrical Circuits I Lecture 10
Transcript of Electrical Circuits I Lecture 10
Electric Circuits I “Dr. Ahmed El-Shenawy”
<Dr Hadi El-Helw><Dr Ahmed El-Shenawy>
Electrical Circuits I Lecture 10
Electric Circuits I “Dr. Ahmed El-Shenawy”
Direct Current (DC)
Direct Current (DC) always flows in the same direction, but it may increase and decrease. A DC voltage is always positive (or always negative), but it may increase and decrease. Electronic circuits normally require a steady DC supply which is constant at one value or a smooth DC supply which has a small variation called ripple.
Steady DC
Smooth DC
Varying DC
Electric Circuits I “Dr. Ahmed El-Shenawy”
All the industrial power-distribution networks operate with alternating currents.
Alternating Current (AC)
Electric Circuits I “Dr. Ahmed El-Shenawy”
The magnitude of the emf and current varies with time:
– Maximum when coil is perpendicular to the field– Zero when the coil is parallel to the field
Electric Circuits I “Dr. Ahmed El-Shenawy”
Alternating Current (AC) flows one way, then the other way, continually reversing direction.
An AC voltage is continually changing between positive (+) and negative (-).
The rate of changing direction is called the frequency of the AC and it is measured in hertz (Hz) which is the number of forwards-backwards cycles per second.
Electric Circuits I “Dr. Ahmed El-Shenawy”
sinmA
General format for the Sinusoidal voltage or current
The basic mathematical format for the sinusoidal waveform is:
Whereθ =ωtω The angular velocity of the rotating vectort Time
ω=2 π f
Am The peak value of the waveformθ is the unit of the horizontal axis
Thus, we have consider only sine waves that have maxima value at π/2 and 3 π/2 . With a zero value at 0, π , and 2 π as shown in the previous fig. if the waveform is shifted to the right or left of θ o, the expression becomes
Where θ is the angel in degrees that the waveform has been shifted
)sin()( tVtV m
tVtV m sin)(
)sin()( tVtV m
)sin()( tVtV m
If the wave form crosses the horizontal axis with positive going slope 90o, it is called a cosine wave.
tt cos)90sin(
Electric Circuits I “Dr. Ahmed El-Shenawy”
The average (mean) value of a wave
The average value of an alternating current is equal to the steady (DC) value which transfers same charge to the circuit within a specific period.
T
av dttiT
I0
)(1
0cos2
sin21
20
2
0
m
av
mav
II
dII
In the case of a symmetrical alternating current (i.e. One whose two-half cycle are exactly similar, whether sinusoidal or non-sinusoidal), the average value over a complete cycle is zero.
Electric Circuits I “Dr. Ahmed El-Shenawy”
average value over one (or more) cycles of a sine wave is clearly zero.however, it is often useful to know the average magnitude of the waveform independent of its polarity:
We can think of this as the average value over half a cycle……or as the average value of the rectified signal
mav
mmav
mav
II
III
dII
637.0
2cos
sin21
0
0
Electric Circuits I “Dr. Ahmed El-Shenawy”
Electric Circuits I “Dr. Ahmed El-Shenawy”
Example 1:
Determine the average value of the voltage waveform shown below.
Electric Circuits I “Dr. Ahmed El-Shenawy”
Example 2:
Determine the average value of the voltage waveform shown below.
Electric Circuits I “Dr. Ahmed El-Shenawy”
Example 3:
Determine the average value of the current waveform shown below.
