Reactance

Reactance is a fundamental concept in electrical engineering, playing a crucial role in both AC (alternating current) and DC (direct current) circuits. Reactance arises from the presence of inductance and capacitance, which impede the flow of current differently than resistance. Understanding reactance is essential for analyzing and designing electrical circuits.

In AC circuits, reactance is the opposition to the flow of alternating current caused by inductors and capacitors. Unlike resistance, which dissipates energy, reactance stores and releases energy in the form of magnetic and electric fields.

AC Inductive Reactance (XL)

Formula: XL = 2πfL

Formula Breakdown:

• XL: Inductive reactance (ohms, Ω)
• f: Frequency (hertz, Hz)
• L: Inductance (henrys, H)

Example Calculation:

• Task: Calculate the inductive reactance of a 10 mH inductor at a frequency of 60 Hz.
• Solution: Use the formula XL = 2πfL.
• XL = 2 × π × 60 × 0.01 = 3.77 Ω

AC Capacitive Reactance (XC)

Formula: XC = 1 / (2πfC)

Formula Breakdown:

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

Example Calculation:

• Task: Calculate the capacitive reactance of a 100 μF capacitor at a frequency of 60 Hz.
• Solution: Use the formula XC = 1 / (2πfC).
• XC = 1 / (2 × π × 60 × 100 × 10^-6) = 26.53 Ω

Impedance (Z) in AC Circuits

Impedance is the total opposition to the flow of AC current, combining both resistance (R) and reactance (X).

Formula: Z = √(R² + X²)

Formula Breakdown:

• Z: Impedance (ohms, Ω)
• R: Resistance (ohms, Ω)
• X: Reactance (ohms, Ω)

Example Calculation:

• Task: Calculate the impedance of a circuit with a resistance of 10 Ω and an inductive reactance of 5 Ω.
• Solution: Use the formula Z = √(R² + X²).
• Z = √(10² + 5²) = √(100 + 25) = √125 ≈ 11.18 Ω

Reactance in Three-Phase Systems

In three-phase systems, reactance affects each phase. The calculations for reactance are similar to single-phase systems but applied to each phase.

Formula for Inductive Reactance (XL): XL = 2πfL

Formula for Capacitive Reactance (XC): XC = 1 / (2πfC)

Formula Breakdown:
• XL: Inductive reactance (ohms, Ω)
• XC: Capacitive reactance (ohms, Ω)
• f: Frequency (hertz, Hz)
• L: Inductance (henrys, H)
• C: Capacitance (farads, F)

Example Calculation:

• Task: Calculate the reactance in each phase of a three-phase system with an inductance of 0.2 H, capacitance of 50 μF, and a frequency of 50 Hz.
• Solution: Use the formulas XL = 2πfL and XC = 1 / (2πfC).
• • XL = 2π × 50 Hz × 0.2 H ≈ 62.8 Ω
  • XC = 1 / (2π × 50 Hz × 50 × 10^-6 F) ≈ 63.7 Ω