ELEC 105
Test 4 Review
Peak-to-Peak Value of a Sine Wave
• The peak-to-peak value of a sine wave is the voltage or
current from the positive peak to the negative peak
The peak-to-peak values are represented as:
VPP and IPP
where: VPP = 2 VP and IPP = 2 IP
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RMS Value of a Sine Wave
• The rms (root mean square) value, or effective value, of a sinusoidal
voltage is equal to the dc voltage that produces the same amount of heat in
a resistance as does the sinusoidal voltage
• RMS is the voltage measured with meter
Vrms = Veff = 0.707VP
Irms = Ieff = 0.707IP
Average Value of a Sine Wave
• The average value is the total area under the halfcycle curve divided by the distance in radians of the
curve along the horizontal axis
Vavg = 0.637VP
Iavg = 0.637IP
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Frequency of a Waveform
• Frequency ( f ) is the number of complete cycles that a wave
completes in one second
– The more cycles completed in one second, the higher the frequency
• Frequency is measured in hertz (Hz)
• Relationship between frequency ( f ) and period (T) is:
1
1
f=
Hz =
T
s
Period of a Waveform
• The time required for a sine wave to complete one full cycle is
called the period (T)
– A cycle consists of one complete positive and one complete negative
alternation
– The period of a sine wave can be measured between any two corresponding
points on the waveform
T=
1
f
s=
1
Hz
f=
1
T
Hz =
1
s
3
How a Capacitor Stores Energy
• A capacitor is an electrical device constructed of two
parallel plates separated by an insulating material
called the dielectric
• A capacitor stores energy in the electric field that is
established by the opposite charges on the two plates
• C is the symbol used to denote capacitance
• The farad F is the unit of measurement.
Capacitors in Series
C1 C2
C1 + C2
(100 pF ) ( 330 pF )
CT =
100 pF + 330 pF
CT =
CT = 76.74 pF
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Capacitors in Parallel
CT = C1 + C2
CT = 330 pF + 220 pF
CT = 550pF
The Basic Inductor
• When a length of wire is formed onto a coil, it becomes an
inductor
• Magnetic lines of force around each loop in the winding of
the coil effectively add to the lines of force around the
adjoining loops,
• An inductor stores energy in the electromagnetic field within
and around the coil
• The symbol for inductance is L and unit of measurement is
H - the henry
5
Capacitive Reactance, XC
• Capacitive reactance (XC) is the opposition to sinusoidal
current, expressed in ohms
• The rate of change of voltage is directly related to frequency
• As the frequency increases, the rate of change of voltage
increases, and thus current ( i ) increases
• An increase in i means that there is less opposition to current
(XC is less)
• XC is inversely proportional to i and to frequency
• The relationship between capacitive reactance, capacitance and
frequency is:
XC = - j
1
2πf C
where j = -1
XC is in ohms (Ω)
f is in hertz (Hz)
C is in farads (F)
Inductive Reactance, XL
• Inductive reactance is the opposition to
sinusoidal current, expressed in ohms
• The inductor offers opposition to current, and
that opposition varies directly with frequency
• The formula for inductive reactance, XL, is:
XL = j 2 π f L
• The analysis of the RL circuit is the same for
the RC except that the all the signs of the
imaginary quantities are the opposite
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Impedance of Series RLC Circuits
• A series RLC circuit contains both inductance reactance and
capacitance reactance
• Since XL and XC are antiphase, the total reactance (XX) is
smaller than the smallest reactance
• XX = +jXL -jXC
Z = R + jXL - jXC
Z = R + jXX
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