Capacitance

3-Phase Capacitive Reactance Calculation

Capacitance is the ability of a component or circuit to store and release electrical energy in the form of an electric charge. It is measured in farads (F) and is influenced by factors such as the surface area of the plates, the distance between them, and the dielectric material used.

Capacitance is crucial in various industrial applications, including:

Power Factor Correction

Capacitors are used to improve the power factor in AC power systems, reducing energy losses and improving efficiency.

Energy Storage

Capacitors store energy for applications such as backup power supplies and energy harvesting.

Filtering

Capacitors are used in filters to block or pass specific frequency ranges, essential for signal processing and power quality improvement.

Motor Start and Run

Capacitors are used in motor circuits to improve starting torque and running efficiency.

Capacitance in DC Circuits

In DC circuits, capacitors charge up to the supply voltage and then act as open circuits, blocking any further direct current. The relationship between charge (Q), capacitance (C), and voltage (V) is given by:

Formula: Q = C × V

Formula Breakdown:

Q: Charge (coulombs, C)
C: Capacitance (farads, F)
V: Voltage (volts, V)

Example Calculation:

Task: Calculate the charge stored in a capacitor with a capacitance of 100 μF and a voltage of 12 V.
Solution: Use the formula Q = C × V.
Q = 100 × 10^-6 F × 12 V = 1.2 × 10^-3 C = 1.2 mC

AC Capacitive Reactance Calculation

In AC circuits, capacitors continuously charge and discharge as the voltage alternates. The capacitive reactance (X_C) is given by:

Formula: X_C = 1 / (2πfC)

Formula Breakdown:

X_C: Capacitive reactance (ohms, Ω)
f: Frequency (hertz, Hz)
C: Capacitance (farads, F)

Example Calculation:

Task: Calculate the capacitive reactance and impedance of an AC circuit with a capacitance of 50 μF, a frequency of 60 Hz, and a resistance of 10 Ω.
Solution: Use the formulas X_C = 1 / (2πfC)

X_C = 1 / (2π × 60 Hz × 50 × 10^-6 F) ≈ 53 Ω

3-Phase Capacitive Reactance Calculation

In three-phase systems, capacitors are often used for power factor correction and energy storage. The calculations for capacitive reactance and impedance are similar to single-phase systems but applied to each phase.

Formula: X_C = 1 / (2πfC)

Formula Breakdown:

X_C: Capacitive reactance (ohms, Ω)
f: Frequency (hertz, Hz)
C: Capacitance (farads, F)

Example Calculation:

Task: Calculate the capacitive reactance in each phase of a three-phase system with a capacitance of 20 μF, a frequency of 50 Hz, and a resistance of 15 Ω.
Solution: Use the formula X_C = 1 / (2πfC).
- X_C = 1 / (2π × 50 Hz × 20 × 10^-6 F) ≈ 159 Ω

3-Phase Total Impedance Calculation

The total impedance (Z) in each phase of a three-phase system is given by:

Formula: Z = √(R² + X_C²)

Formula Breakdown:

Z: Impedance (ohms, Ω)
R: Resistance (ohms, Ω)
X_C: Capacitive reactance (ohms, Ω)

Example Calculation:

Task: Calculate the capacitive impedance in each phase of a three-phase system with a capacitance of 20 μF, a frequency of 50 Hz, and a resistance of 15 Ω.
Solution: Use the formula Z = √(R² + X_C²).
- Z = √(15 Ω)² + (159 Ω)² ≈ 160 Ω

Capacitor Unit Conversion Chart

Microfarads (µF)	Nanofarads (nF)	Picofarads (pF)	Farads (F)
1 µF = 1,000,000 nF	1 nF = 1,000 pF	1 pF = 10^-12 F	1 F = 10^6 µF
0.001 µF = 1,000 nF	1 nF = 0.001 µF	1 pF = 0.001 nF	1 F = 1,000,000 µF
10 µF = 10,000 nF	10 nF = 10,000 pF	1 nF = 0.000001 µF	1 F = 1,000,000,000 pF
0.1 µF = 100 nF	100 nF = 100,000 pF	1 pF = 0.000000001 µF	1 F = 0.000001 µF