Inductors and RL Circuits

Inductors and RL Circuits

What Is an Inductor?

An inductor is a coil of wire that stores energy in a magnetic field when current flows through it. The core property of an inductor is self-inductance, measured in henries (H). One henry is defined as the inductance that produces one volt of back-EMF when the current through it changes at a rate of one ampere per second. In practical circuits you will more often work with millihenries (mH) and microhenries (µH).

When current through a coil changes, the changing magnetic flux induces a voltage that opposes that change — a principle stated by Lenz's Law. This opposing voltage is called the back-EMF or counter-EMF. The faster the current tries to change, the greater the back-EMF the inductor produces.

Types of Inductors

Inductors come in several forms. Air-core inductors have no magnetic core material and are used at radio frequencies. Iron-core inductors use laminated steel and are common in power-frequency transformers and filters. Ferrite-core inductors use a ceramic magnetic material and are used across a wide range of audio and RF frequencies. Toroidal inductors wound on a donut-shaped core contain the magnetic field well and minimize interference with nearby components. The choice of core material directly affects the inductance value and the frequency range where the inductor performs well.

Inductive Reactance

In an AC circuit, an inductor opposes the flow of alternating current through a property called inductive reactance (X_L), measured in ohms (Ω). Unlike resistance, inductive reactance does not dissipate power as heat — it returns energy to the circuit each half-cycle.

The formula for inductive reactance is:

X_L = 2πfL

where:

• f = frequency in hertz (Hz)
• L = inductance in henries (H)
• 2π ≈ 6.283

As frequency increases, X_L increases proportionally. As inductance increases, X_L also increases. This is why inductors block high-frequency signals while passing low-frequency or DC signals — the basis of low-pass filter design used throughout electronics and telecommunications.

Phase Relationship in RL Circuits

In a purely resistive circuit, voltage and current are in phase. When you add an inductor in series, the inductor's back-EMF shifts the phase relationship. In an ideal inductor carrying AC, voltage leads current by 90°. In a real RL series circuit, the phase angle (θ) between the source voltage and the current falls between 0° and 90°, depending on the ratio of reactance to resistance.

On an oscilloscope with dual channels, you can observe this relationship directly. Channel 1 (CH1) is connected across the resistor; the voltage waveform on CH1 is proportional to circuit current because Ohm's Law applies to the resistor (V_R = IR). Channel 2 (CH2) displays the source voltage. Because V_R is in phase with current, CH1 shows the current waveform effectively. You will see CH2 (source voltage) leading CH1 (current proxy) by the phase angle of the circuit.

RL Time Constant

When a DC voltage is suddenly applied to a series RL circuit (as a square wave simulates), the current does not rise instantly. It rises exponentially toward its final value. The RL time constant (τ) defines how quickly this happens:

τ = L / R

where:

• τ = time constant in seconds (s)
• L = inductance in henries (H)
• R = resistance in ohms (Ω)

After one time constant, the current reaches approximately 63.2% of its final steady-state value. After five time constants, the current is considered fully established (>99%). On the oscilloscope, you can measure τ by using the cursors to find the time at which the rising voltage across the resistor reaches 63.2% of its peak value, since V_R mirrors current.

In telecommunications and electronics, RL time constants affect pulse shaping, filter roll-off, and relay response times — all relevant to your work as a technician.

Safety in This Lab

This lab uses low-voltage bench equipment, but good habits learned here transfer to higher-voltage work:

• Inspect all leads and coils before energizing. Frayed insulation on a wire near a sharp ferrite edge can cause a short or a cut.
• Do not exceed the voltage rating of inductors. Core saturation or insulation breakdown can damage the component and the function generator.
• Function generators and oscilloscopes have chassis grounds tied to the building ground. Avoid creating unintended ground loops by connecting probes carelessly; this can give false readings or damage equipment.
• ESD (electrostatic discharge) can damage sensitive components. Touch a grounded metal surface before handling components.
• Tie back loose hair and remove dangling jewelry when working around any energized bench equipment.
• Follow your program's standard lockout/tagout (LOTO) procedure before modifying any circuit that is part of a larger powered system — a habit that scales to industrial work covered in your ETA CET studies.