HD Animation: RLC Circuit

The animation illustrates the operation of an RLC circuit. The total voltage, frequency, and nominal values of the electronic components are interactively adjustable.

Instructions for Use

The windows, like in all animations, can be enlarged or reduced by clicking.

After starting the application, you can view the animation in fullscreen mode. To do so, click “View” and then “Fullscreen”:

To exit fullscreen mode, press the Esc key.

Description of the Animation

The letters R, L, and C refer to the electronic components: resistance (R), inductance (L), and capacitance (C). In the animation, besides RLC circuits, R-, L-, C-, LC-, RC-, and RL-circuits can also be configured. To add a component, activate one of the checkboxes below.

The top-left window shows the circuit diagram. Below it is the phasor diagram. The phasor diagram clearly illustrates how the individual voltage drops can be calculated geometrically.

It provides a visual representation of the phase shifts in the circuit. The graph at the bottom right displays the time-dependent course of the partial voltages.

Step by Step: What Does the Animation Show?

To get the most out of the animation, we recommend the following experiments:

1. Activate R only: Enable only the resistor. Observe that current and voltage are in phase – the phasors in the phasor diagram point in the same direction.
2. Activate L only: Switch to a pure inductance. The current lags the voltage by 90° – in the phasor diagram, the current phasor is perpendicular to the voltage phasor.
3. Activate C only: Switch to the capacitor alone. Here, the current leads the voltage by 90° – exactly the opposite of the inductor.
4. LC circuit and resonance: Enable both L and C simultaneously and slowly change the frequency. Watch how the L and C phasors in the phasor diagram cancel each other out as you approach the resonant frequency.
5. Full RLC circuit: Enable all three components. Vary the resistance R and observe how the damping affects both the phasor diagram and the time-domain voltage waveform.
6. Sweep the frequency: With the RLC circuit active, change the frequency from low to high and observe the transition from capacitive through resistive to inductive behaviour.

What Happens in an RLC Circuit – An Intuitive Explanation

Before diving into the formulas, it is worth understanding the basic principle: in an RLC circuit, three components work together, each storing and releasing energy in a different way.

The capacitor (C) stores energy in an electric field – similar to a compressed spring. The inductor (L) stores energy in a magnetic field – comparable to a heavy pendulum in motion. These two components continuously exchange energy back and forth: when the capacitor discharges, the inductor builds up its magnetic field, and vice versa. This interplay creates an oscillation.

The resistor (R) converts some of that energy into heat, thereby damping the oscillation – like friction on a pendulum that gradually brings it to rest.

When driven by an AC voltage, the circuit’s behaviour depends strongly on the frequency: at a specific frequency (the resonant frequency) the inductor and capacitor oscillate in perfect harmony, and the current reaches its maximum. This is exactly the behaviour you can observe in the animation.

Physical Background

The impedance (total resistance) of a series RLC circuit is:

\[ Z = \sqrt{R^2 + (X_L – X_C)^2} \]

• Z: impedance (total resistance)
• R: ohmic resistance
• X_L: inductive reactance
• X_C: capacitive reactance

The reactances of the inductor and capacitor are:

\[ X_L = 2\pi f L \qquad X_C = \frac{1}{2\pi f C} \]

• X_L: inductive reactance
• X_C: capacitive reactance
• f: frequency
• L: inductance of the coil
• C: capacitance of the capacitor

At the resonant frequency the reactances cancel out (X_L = X_C), the current reaches its maximum, and voltage and current are in phase:

\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]

• f₀: resonant frequency
• L: inductance
• C: capacitance

Understanding Resonance – An Analogy

Resonance is easiest to understand by thinking of a playground swing: if you push the swing at exactly the right moment – just as it reaches its highest point – the oscillation grows larger with minimal effort. Push at the wrong rhythm, and you actually slow the swing down.

In an RLC circuit, the AC voltage source plays the role of the push. The resonant frequency f₀ is the “right rhythm”: at this frequency, the effects of the inductor and capacitor cancel each other out, and current flows almost unimpeded – limited only by the ohmic resistance R.

Subcircuit Behaviour at a Glance

The animation supports various circuit configurations. The table below summarises the behaviour of each:

Circuit	Impedance	Phase Shift	Key Feature
R	Z = R	0° (in phase)	Purely ohmic, frequency-independent
L	Z = XL	+90° (current lags)	Impedance rises with frequency
C	Z = XC	−90° (current leads)	Impedance falls with frequency
RL	Z = √(R² + XL²)	0° to +90°	Low-pass behaviour
RC	Z = √(R² + XC²)	0° to −90°	High-pass behaviour
LC	Z = |XL – XC|	+90° or −90°	At resonance: Z = 0 (ideal)
RLC	Z = √(R² + (XL – XC)²)	−90° to +90°	At resonance: Z = R (minimum)

Frequency Response and Filter Behaviour

An RLC series circuit acts as a bandpass filter: it allows signals near the resonant frequency to pass almost unimpeded while attenuating frequencies well above or below it.

The principle: at low frequencies, the capacitive reactance X_C dominates – the capacitor blocks current flow. At high frequencies, the inductive reactance X_L dominates – the inductor impedes the current. Only at the resonant frequency do these two effects cancel, allowing maximum current to flow.

This behaviour underpins many real-world applications:

• Radio receivers: A tuned circuit selects exactly one station (one frequency) from the entire spectrum.
• Audio equalisers: Bandpass filters isolate specific frequency ranges (bass, midrange, treble) for targeted boost or cut.
• Signal processing: In telecommunications, RLC circuits filter noise from useful signals.

You can observe the filter effect in the animation by slowly varying the frequency and watching the current in the waveform diagram: at the resonant frequency, the amplitude reaches its peak.

Quality Factor Q – How Sharp Is the Resonance?

The quality factor (or Q factor) describes how “sharp” or “narrow” the resonance curve of an RLC circuit is. A high Q value means a narrow, pronounced resonance peak; a low Q value produces a broad, flat curve.

For an RLC series circuit:

\[ Q = \frac{1}{R} \sqrt{\frac{L}{C}} \]

The quality factor depends on all three component values:

• Small resistance R → high Q → sharp resonance
• Large resistance R → low Q → broad resonance

In practice, the quality factor determines how selective a filter is: a radio receiver requires a high Q to cleanly separate adjacent stations. A loudspeaker crossover, on the other hand, deliberately uses a low Q to pass a wider frequency range.

Try it in the animation: With the full RLC circuit active, change the resistance R. At low R, the circuit responds very sensitively to frequency changes near resonance – at high R, the response becomes “sluggish” and less pronounced.

Format and Use

Format: Executable program for Windows and Mac. Download available via contact form.

Use case: Optimized for teacher-led use on large screens and projectors. Lossless scaling.

In the browser: An interactive web version is available for use directly in the browser.

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Overview and Download

Title	RLC Circuits
Target Audience	Teachers and Lecturers
Platforms	Microsoft® Windows® Apple® Macintosh® (version-dependent)
Features	Full-screen mode Lossless scaling Large screens and projectors supported
License	Freeware
Download	Contact

Sources

Technical drawing based on Thomas Rösel: http://www.uni-muenster.de/EUREGIO-team/team/animationen/

Authoring tool (control elements included): Adobe Animate

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