---
title: "RL Filter | Electrical Circuits and Systems II"
description: "RL Filter in Electrical Circuits and Systems II is a resistor-inductor passive filter that shapes signal frequencies as a low-pass or high-pass circuit."
canonical: "https://fiveable.me/electrical-circuits-systems-ii/key-terms/rl-filter"
type: "key-term"
subject: "Electrical Circuits and Systems II"
unit: "Unit 8"
---

# RL Filter | Electrical Circuits and Systems II

## Definition

An RL filter is a passive circuit with a resistor and inductor that shapes frequency response. In Electrical Circuits and Systems II, you use it to pass certain frequencies and attenuate others.

## What It Is

An RL filter is a first-order passive filter built from a resistor and an inductor. In Electrical Circuits and Systems II, you usually see it as a simple way to make a circuit respond differently to low and high frequencies without using any active components.

The big idea is that the inductor resists changes in current, and that resistance changes with frequency. At low frequencies, an inductor behaves more like a short circuit. At high frequencies, its impedance increases, so it blocks more current. That frequency-dependent behavior is what gives the filter its shape.

An RL filter can be arranged as a low-pass or high-pass filter depending on where you take the output. If the output is taken across the resistor, the circuit can act like a low-pass filter. If the output is taken across the inductor, it can act like a high-pass filter. The same two components are present, but the output point changes what you measure.

The cutoff frequency is the point where the output starts dropping noticeably, usually at the -3 dB point. For a basic RL filter, the cutoff depends on both R and L, often written as f_c = R / (2πL). That means changing either component changes where the filter starts separating frequencies.

The time constant also shows up in transient response. For an RL circuit, τ = L / R. A larger inductance or smaller resistance means the current changes more slowly after a step input. That is why RL filters show up in both frequency-response problems and transient-analysis problems in this course.

A common mistake is treating the inductor like a fixed resistor. It is not fixed. Its impedance depends on frequency, which is exactly why the filter works. If you keep that in mind, the circuit becomes much easier to analyze with Ohm's law, phasors, and Bode plots.

## Why It Matters

RL filters show up whenever you need to predict how a circuit treats changing signals, not just steady DC. In Electrical Circuits and Systems II, that means they connect your earlier circuit tools to frequency response, impedance, and transient behavior all at once.

This term also helps you recognize what the math is doing in problem sets. If you are given R, L, and an output location, you need to decide whether the circuit behaves like a low-pass or high-pass filter, then compute the cutoff frequency and explain the response. That is a very different skill from simply memorizing that inductors resist change.

RL filters are also a bridge to Bode plots and AC analysis. Once you know how the output changes with frequency, you can sketch gain and phase curves instead of guessing them. That matters when you are comparing circuits in lab data, checking whether a signal is being smoothed or blocked, or explaining why a waveform looks rounded after passing through an inductor-based network.

They also prepare you for more advanced filter design. Even when the course moves on to RLC or LC circuits, the same habits still apply: identify the reactive element, find the cutoff behavior, and read the circuit from its impedance. RL filters are the simplest place to practice that setup.

## Connections

### Time Constant

The RL time constant, τ = L / R, tells you how fast current changes after a step input. In filter problems, it helps you predict the transient response, especially right after switching. If τ is large, the circuit reacts slowly; if τ is small, it settles faster. That same quantity is tied to the circuit's frequency behavior.

### Impedance

Impedance is the frequency-dependent opposition to AC in the inductor. RL filters work because the inductor's impedance increases with frequency, changing how much signal reaches the output. When you analyze the circuit in the frequency domain, impedance is the main tool that replaces simple resistance thinking.

### [Cutoff Frequency](/electrical-circuits-systems-ii/key-terms/cutoff-frequency)

The cutoff frequency is where the RL filter begins to significantly attenuate part of the signal. For a basic RL filter, it depends on both the resistor and inductor values, so changing either shifts the transition point. In homework and lab work, this is usually the number you calculate to describe where the filter starts working.

### [high-pass filter](/electrical-circuits-systems-ii/key-terms/high-pass-filter)

An RL circuit can be wired as a high-pass filter when the output is taken across the inductor. That setup passes higher frequencies better because the inductor's impedance rises with frequency. If you mix up the output location, you may label the same circuit incorrectly, so always check where the output is measured.

## On the AP Exam

A quiz or problem-set question will usually give you R, L, an input signal, and the output location, then ask you to identify the filter type, find the cutoff frequency, or describe the gain at low and high frequencies. You may also be asked to sketch a Bode magnitude plot or explain the phase trend.

If the circuit is drawn in time-domain form, you might need to use the time constant to predict how fast the current or output settles after a switch closes. If it is given in AC steady-state form, you use impedance to decide how the inductor behaves at different frequencies. The main move is to connect the circuit layout to the frequency response, not just to name the parts.

## RL Filter vs RLC Filter

An RL filter uses only one reactive element, the inductor, so it is first-order. An RLC filter adds a capacitor, which gives the circuit second-order behavior and can create resonance. If you see a capacitor in the network, you are no longer dealing with a simple RL filter.

## Key Takeaways

- An RL filter is a passive filter made from a resistor and an inductor, and it shapes signals by frequency.
- The inductor's impedance changes with frequency, which is why the circuit can act like a low-pass or high-pass filter.
- The cutoff frequency tells you where the circuit starts attenuating part of the signal, and it depends on both R and L.
- The time constant, τ = L / R, describes the transient response and shows how quickly the circuit reacts after a change.
- In this course, you use RL filters to read Bode plots, analyze AC behavior, and predict what happens to a waveform in a real circuit.

## FAQs

### What is an RL Filter in Electrical Circuits and Systems II?

An RL filter is a passive circuit made from a resistor and an inductor that passes some frequencies more easily than others. In this course, it shows up as a first-order filter, so you use it to study frequency response, cutoff frequency, and transient behavior.

### Is an RL filter low-pass or high-pass?

It can be either, depending on where you take the output. Output across the resistor can give you a low-pass response, while output across the inductor gives you a high-pass response. The components are the same, but the measurement point changes the result.

### How do you find the cutoff frequency of an RL filter?

For a basic RL filter, the cutoff frequency is usually f_c = R / (2πL). That formula comes from the point where the inductor's reactance matches the resistance in the circuit. In homework, this is often the number you use to describe where the filter starts attenuating.

### What is the difference between an RL filter and an RLC filter?

An RL filter has one reactive element, the inductor, so it is first-order. An RLC filter adds a capacitor, which makes the circuit second-order and can produce resonance and a sharper response. If you are only dealing with R and L, stick with first-order filter behavior.

## Related Study Guides

- [8.2 First-order and second-order passive filters](/electrical-circuits-systems-ii/unit-8/first-order-second-order-passive-filters/study-guide/W94UYjTFg0BULtWT)

## About This Document

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