There are many natural causes of capacitance in AC power circuits

There are many natural causes of capacitance in AC power circuits,
such as transmission lines, fluorescent lighting, and computer
monitors. Normally, these are counteracted by the inductors
previously discussed. However, where capacitors greatly outnumber
inductive devices, we must calculate the amount of capacitance to add
or subtract from an AC circuit by artificial means.
EO 1.5 DEFINE capacitive reactance (XC).
EO 1.6 Given the operating frequency (f) and the value of
capacitance (C), CALCULATE the capacitive reactance
(XC) of a simple AC circuit.

EO 1.7 DESCRIBE the effect on phase relationship between
current (I) and voltage (E) in a capacitive circuit.
EO 1.8 DRAW a simple phasor diagram representing AC
current (I) and voltage (E) in a capacitive circuit.
Capacitors
The variation of an alternating voltage applied to
Figure 3 Voltage, Charge, and Current in
a Capacitor
a capacitor, the charge on the capacitor, and the
current flowing through the capacitor are
represented by Figure 3.
The current flow in a circuit containing
capacitance depends on the rate at which the
voltage changes. The current flow in Figure 3 is
greatest at points a, c, and e. At these points, the
voltage is changing at its maximum rate (i.e.,
passing through zero). Between points a and b,
the voltage and charge are increasing, and the
current flow is into the capacitor, but decreasing
in value. At point b, the capacitor is fully
charged, and the current is zero. From points b
to c, the voltage and charge are decreasing as the
capacitor discharges, and its current flows in a
direction opposite to the voltage. From points c
to d, the capacitor begins to charge in the
opposite direction, and the voltage and current are
again in the same direction.
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CAPACITANCE Basic AC Reactive Components
At point d, the capacitor is fully charged, and the current flow is again zero. From points d to
e, the capacitor discharges, and the flow of current is opposite to the voltage. Figure 3 shows
the current leading the applied voltage by 90°. In any purely capacitive circuit, current leads
applied voltage by 90°.
Capacitive Reactance
Capacitive reactance is the opposition by a capacitor or a capacitive circuit to the flow of
current. The current flowing in a capacitive circuit is directly proportional to the capacitance and
to the rate at which the applied voltage is changing. The rate at which the applied voltage is
changing is determined by the frequency of the supply; therefore, if the frequency of the
capacitance of a given circuit is increased, the current flow will increase. It can also be said that
if the frequency or capacitance is increased, the opposition to current flow decreases; therefore,
capacitive reactance, which is the opposition to current flow, is inversely proportional to
frequency and capacitance. Capacitive reactance XC, is measured in ohms, as is inductive
reactance. Equation (8-3) is a mathematical representation for capacitive reactance.
X (8-3) C
1
2pfC
where
f = frequency (Hz)
p = ~3.14
C = capacitance (farads)
Equation (8-4) is the mathematical representation of capacitive reactance when capacitance is
expressed in microfarads (μF).
X (8-4) C
1,000,000
2pfC
Equation (8-5) is the mathematical representation for the current that flows in a circuit with only
capacitive reactance.
I E (8-5)
XC
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Basic AC Reactive Components CAPACITANCE
where
I = effective current (A)
E = effective voltage across the capacitive reactance (V)
XC = capacitive reactance (W)
Example: A 10μF capacitor is connected to a 120V, 60Hz power source (see Figure 4).
Find the capacitive reactance and the current flowing in the circuit. Draw the
phasor diagram.
Figure 4 Circuit and Phasor Diagram
Solution:
1. Capacitive reactance
XC
1,000,000
2pfC
1,000,000
(2)(3.14)(60)(10)
1,000,000
3768
XC 265.4W
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CAPACITANCE Basic AC Reactive Components
2. Current flowing in the circuit
I E
XC
120
265.4
I 0.452 amps
3. Phasor diagram showing current leading voltage by 90° is drawn in Figure 4b.
Summary
Capacitive reactance is summarized below.
Capacitive Reactance Summary
Opposition to the flow of alternating current caused by capacitance is called
capacitive reactance (XC).
The formula for calculating XC is:
XC
1
2pfC
Current (I) leads applied voltage by 90o in a purely capacitive circuit.
The phasor diagram shows the applied voltage (E) vector leading (below) the
current (I) vector by the amount of the phase angle differential due to the
relationship between voltage and current in a capacitive circuit.
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Basic AC Reactive Components IMPEDANCE
IMPEDANCE
Whenever inductive and capacitive components are used in an AC
circuit, the calculation of their effects on the flow of current is
important.
EO 1.9 DEFINE impedance (Z).
EO 1.10 Given the values for resistance (R) and inductance (L)
and a simple R-L series AC circuit, CALCULATE the
impedance (Z) for that circuit.
EO 1.11 Given the values for resistance (R) and capacitance (C)
and a simple R-C series AC circuit, CALCULATE the
impedance (Z) for that circuit.
EO 1.12 Given a simple R-C-L series AC circuit and the values
for resistance (R), inductive reactance (XL), and
capacitive reactance (XC), CALCULATE the impedance
(Z) for that circuit.
EO 1.13 STATE the formula for calculating total current (IT) in
a simple parallel R-C-L AC circuit.
EO 1.14 Given a simple R-C-L parallel AC circuit and the values
for voltage (VT), resistance (R), inductive reactance (XL),
and capacitive reactance (XC), CALCULATE the
impedance (Z) for that circuit.
Impedance
No circuit is without some resistance, whether desired or not. Resistive and reactive components
in an AC circuit oppose current flow. The total opposition to current flow in a circuit depends
on its resistance, its reactance, and the phase relationships between them. Impedance is defined
as the total opposition to current flow in a circuit. Equation (8-6) is the mathematical
representation for the magnitude of impedance in an AC circuit.
Z R 2 X 2 (8-6)
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IMPEDANCE Basic AC Reactive Components
where
Z = impedance (W)
R = resistance (W)
X = net reactance (W)
The relationship between resistance, reactance, and impedance is shown in Figure 5.
Figure 5 Relationship Between Resistance, Reactance, and Impedance
The current through a certain resistance is always in phase with the applied voltage. Resistance
is shown on the zero axis. The current through an inductor lags applied voltage by 90°; inductive
reactance is shown along the 90° axis. Current through a capacitor leads applied voltage by 90°;
capacitive reactance is shown along the -90° axis. Net reactance in an AC circuit is the
difference between inductive and capacitive reactance. Equation (8-7) is the mathematical
representation for the calculation of net reactance when XL is greater than XC.
X = XL - XC (8-7)
where
X = net reactance (W)
XL = inductive reactance (W)
XC = capacitive reactance (W)
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Basic AC Reactive Components IMPEDANCE
Equation (8-8) is the mathematical representation for the calculation of net reactance when XC
is greater than XL.
X = XC - XL (8-8)
Impedance is the vector sum of the resistance and net reactance (X) in a circuit, as shown in
Figure 5. The angle q is the phase angle and gives the phase relationship between the applied
voltage and the current. Impedance in an AC circuit corresponds to the resistance of a DC
circuit. The voltage drop across an AC circuit element equals the current times the impedance.
Equation (8-9) is the mathematical representation of the voltage drop across an AC circuit.
V = IZ (8-9)
where
V = voltage drop (V)
I = current (A)
Z = impedance (W)
The phase angle q gives the phase relationship between current and the voltage.
Impedance in R-L Circuits
Impedance is the resultant of phasor addition of R and XL. The symbol for impedance is Z.
Impedance is the total opposition to the flow of current and is expressed in ohms. Equation
(8-10) is the mathematical representation of the impedance in an RL circuit.
Z R 2 X (8-10) 2
L
Example: If a 100 W resistor and a 60 W XL are in series with a 115V applied voltage
(Figure 6), what is the circuit impedance?