310102k Inductance and Inductive Reactance 2025(TF)

Instrumentation Technician

Inductance and Inductive Reactance

• Key Components

  • Conducting coil, magnet, and current are foundational elements in understanding inductance.

Objectives

1. Describe the basic inductor (coil).

2. Describe inductance and the factors which affect it.

3. Describe induction and its effects.

4. Explain the effects of an inductor in a DC circuit.

5. Explain the effects of an inductor in an AC circuit.

6. Analyze an AC inductive circuit.

7. Discuss power relationships in an inductive circuit.

Inductance & Inductive Reactance

In a Direct Current Circuit

• An inductor opposes changes in current when the circuit is turned on and off.

In an Alternating Current Circuit

• An inductor continually opposes current changes due to the continuously changing current.

• This opposition is termed inductive reactance.

• Common inductors include coils, motors, and transformers, each with specific inductance values indicating their capability to counteract current change.

Symbols and Units

• Inductance Symbol: L

• Unit of Measurement: Henry (H)

• Example: A coil with an inductance of 0.034 H.

Resistance in Inductors

• Coils possess inherent resistance, represented by the resistor symbol in circuit diagrams.

• In ideal scenarios (pure inductors), resistance can be considered negligible.

Formulas

Resistance Formula

• R = (ρ • l) / A

  • R: Electrical resistance (Ω)

  • ρ: Static resistivity (Ω-m)

  • l: Length of material (m)

  • A: Cross-sectional area (m²)

Inductance Formula

• L = (N² • µ • A) / l

  • L: Inductance

  • N: Number of wire turns

  • µ: Permeability of core

  • A: Cross-sectional area of core

  • l: Length of magnetic path

Faraday’s Law of Induction

• Induced voltage occurs with relative motion between a conductor and a magnetic field.

• Three factors affecting induced voltage in AC generation:

  • RPM of the conductor.

  • Flux density.

  • Angle of the conductor relative to magnetic lines of flux.

Self-Induction & Lenz’s Law

• Lenz’s Law describes that induced voltage polarity must act to oppose the change in original flux, termed counter emf.

Factors Influencing Counter emf

• Determined by:

  • The inductance of the coil.

  • The rate of change of current.

• Cemf = (change of current) • (inductance) / (change of time)

Time Constant in DC Circuits

• Time Constant (τ) = Inductance (L) / Resistance (R)

• Steady state current established after 5 time constants.

• During each time constant, current changes by 63.2% of remaining current.

AC Circuit Dynamics

• The impact of inductance on AC circuits is significant; inductive reactance (XL) is defined as:

  • XL = 2πFL

• Low vs. High inductance affects the AC circuit performance.

• The frequency affects inductive reactance as demonstrated by: XL = 2πFL.

Power Relationships in an Inductive Circuit

• In AC circuits, coils react to changing currents, opposing changes, thus consuming energy stored in the electromagnetic field, which is returned to the circuit, regarded as wasted energy (reactive power).

• Reactive Power (Q):

  Q = Reactive Voltage x Reactive Current

  • QXL = I² • XL

  • QXL = Voltamp Reactance

Visual Representations

• Figures demonstrate symbols for inductance, inductive circuits, and the comparison of resistance vs. inductive reactance in AC circuits.