Inductance, Inductive Reactance, and RL Circuits

What Is Inductance?

An inductor is a coil of wire that stores energy in a magnetic field when current flows through it. The property that describes how strongly a coil opposes a change in current is called inductance, symbol L, measured in henries (H). A larger coil with more turns and an iron core has higher inductance than a small air-core coil with few turns.

In a DC circuit, an inductor acts like a short piece of wire once current is steady — its only opposition is the small DC resistance of the wire itself. In an AC circuit, everything changes, because AC is constantly reversing, meaning the current is always changing. That changing current constantly collapses and rebuilds the magnetic field, and that changing field induces a voltage that opposes the change. This opposition is called inductive reactance.

Inductive Reactance (X_L)

Inductive reactance is the AC opposition an inductor presents to current flow. It is measured in ohms (Ω), just like resistance, but it behaves differently — no heat is produced by pure reactance. The formula is:

> X_L = 2πfL

Where:

• X_L = inductive reactance in ohms (Ω)
• π ≈ 3.1416
• f = frequency in hertz (Hz)
• L = inductance in henries (H)

Two important conclusions follow directly from this formula:

1. Higher frequency → higher X_L. The current changes faster, so the inductor fights back harder.

2. Larger inductance → higher X_L. More magnetic flux linkage means more opposition.

At the US power-line frequency of 60 Hz, a 100 mH (0.1 H) inductor has X_L = 2π × 60 × 0.1 ≈ 37.7 Ω.

Why Voltage Leads Current by 90°

In a pure inductor, the induced voltage is greatest when the current is changing most rapidly (at the zero crossing), and the induced voltage is zero when the current is at its peak (not changing at that instant). This timing relationship means the voltage waveform reaches its peak one-quarter cycle (90°) before the current waveform. Put another way, current lags voltage by 90° in a pure inductor.

A useful memory aid: ELI — in an inductive (L) circuit, Voltage (E) comes before Current (I).

RL Series Circuits and Impedance

When a resistor and an inductor are connected in series, the total opposition to AC current is called impedance, symbol Z, also in ohms. You cannot simply add R and X_L the way you add two resistances, because they are 90° out of phase with each other. Instead, use the Pythagorean theorem:

> Z = √(R² + X_L²)

The phase angle θ between voltage and current in the RL circuit is:

> θ = arctan(X_L / R)

In a purely resistive circuit θ = 0°; in a purely inductive circuit θ = 90°. A real RL circuit falls somewhere between those extremes.

Reading Your Measurements

In the lab you will use a true-RMS DMM to measure AC voltages. A true-RMS meter correctly reads the effective value of any AC waveform — this is important because standard average-responding meters are calibrated for a perfect sine wave and can read low on distorted signals from function generators.

You will also use a dual-trace oscilloscope to see both the source voltage and the resistor voltage at the same time. The resistor voltage is in phase with the current (Ohm's law — V_R = I × R, no phase shift). By comparing the resistor trace to the source trace you can directly observe how much the current lags the source voltage.

Lab Safety

• Bench transformer and function generator outputs in this lab are low-voltage AC. Even so, treat every energized conductor as a shock hazard. Do not reach into a live circuit.
• Build and check your circuit with power OFF. Have your instructor verify the wiring before you apply power.
• Lockout/tagout awareness: Although bench supplies have simple on/off switches, the professional habit of de-energizing before working on a circuit must be practiced every time — it is the foundation of LOTO procedures you will use on the job under OSHA standards.
• Oscilloscope probes: Keep probe ground clips connected to the same reference point to avoid creating a short circuit through the scope's chassis ground.
• Inspect components: Check for cracked or burned inductors and resistors before use. Do not use damaged components.
• Wear safety glasses in the lab at all times.

Connecting Theory to Your Credentials

NCCER Electrical Levels 1 and 2 cover AC theory and the math behind inductive circuits — material that appears on NCCER written assessments. Understanding impedance also prepares you for motor and transformer topics in Levels 3 and 4. Your state journeyman exam will expect you to analyze AC circuits correctly. OSHA 10 training reinforces the safe work habits practiced in every lab session.