40 Electrical Power Systems Technology
in the purely inductive circuit. As shown in Figure 2-13B, the positive and
negative power waveforms will cancel one another out.
Since all circuits contain some resistance, a more practical circuit is
the esistive-capacitive (RC) r circuit, shown in Figure 2-14A. In an RC circuit,
the current leads the voltage by some phase angle between 0° and 90°.
As capacitance increases with no corresponding increase in resistance, the
phase angle becomes greater. The waveforms of Figure 2-14B show an RC
circuit in which current leads voltage by 30°. This circuit is similar to the
RL circuit in Figure 2-12. Power is converted in the circuit except during
the 00 to 30° interval and the 180° to 210° interval. In the RC circuit shown,
most of the electrical energy supplied by the source is converted into an-
other form of energy in the load.
Due to the electrostatic field that is developed around a capacitor, an
opposition to the flow of AC exists. This opposition is known as capacitive
reactance (XC). Capacitive reactance is expressed as:
1
XC = ———
2 πfC
where:
XC is the capacitive reactance in ohms,
2 π is the mathematical expression of one sine wave (0° to 360°),
f is the frequency of the source in hertz, and
C is the capacitance in farads.
Sample Problem:
Given: frequency = 50 Hz, and capacitance = 200 μF.
Find: capacitive reactance.
Solution:
1
XC = —————————
2 π × 50 × 200–^6
XC = 15.92Ω
VECTOR AND PHASOR DIAGRAMS FOR AC CIRCUITS
In Figures 2-10C, 2-11C, 2-12C, 2-13C and 2-14C, a vector diagram was
shown for each circuit condition that was illustrated. Vectors are straight
lines that have a specific direction and length. They may be used to rep-