Resonance in AC Circuits

Resonance is an important concept in alternating current (AC) circuits, especially in communication systems, radios, and filters. It occurs when a circuit’s inductive and capacitive effects balance each other out, allowing it to respond strongly to a specific frequency.

What Is Resonance?

In an AC circuit, we often use inductors (L) and capacitors (C). These components react differently to changing currents:

• Inductors resist changes in current (they create inductive reactance).

• Capacitors resist changes in voltage (they create capacitive reactance).

At a certain frequency, the effects of the inductor and capacitor cancel each other out. This is called the resonant frequency. At this point, the circuit behaves as if neither the inductor nor the capacitor is there, and only resistance affects the current.

Resonance in a Series RLC Circuit

A series RLC circuit has a resistor (R), inductor (L), and capacitor (C) all connected in a single loop.

At resonance:

• The inductive reactance (XL) = Capacitive reactance (XC)

• The circuit’s impedance is minimum, and the current is maximum.

Resonant Frequency Formula:

$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

Where:

f0​ is the resonant frequency (in hertz)

L is inductance (in henrys)

C is capacitance (in farads)

This formula tells us the frequency at which resonance happens, based on the values of L and C.

What Happens at Resonance?

When a circuit reaches resonance:

• The circuit draws maximum current from the AC source.

• The voltage across the inductor and capacitor can be much higher than the supply voltage.

• The total impedance (resistance to AC) is at its lowest.

• The circuit is said to be “tuned” to that specific frequency.

This is especially useful in tuning radios or selecting a specific signal frequency.

Applications of Resonance

Resonance is used in many electronic systems:

• Radios and TVs – Tuning to a station uses resonance to pick out the correct frequency.

• Filters – Resonant circuits allow certain frequencies to pass while blocking others.

• Oscillators – Circuits that produce AC signals often rely on resonance to set the frequency.

• Power systems – In transformers and transmission lines, resonance affects energy transfer.

Resonance in Parallel Circuits

In a parallel RLC circuit, the inductor and capacitor are connected side by side. At resonance, the circuit draws minimum current from the source, because the current flowing through the inductor and capacitor cancels out.

While the math is slightly different from the series case, the key idea is the same: the circuit responds most strongly at one specific frequency.

Key Differences: Series vs. Parallel Resonance

Why Is Resonance Important?

Resonance is useful because it lets circuits:

• Focus on or respond to a specific frequency.

• Improve signal quality and reduce noise.

• Transfer power efficiently at the desired frequency.

However, it must be used carefully. If not controlled, resonance can cause overvoltage or overheating in circuits.

Summary

Understanding resonance helps you design and analyze AC circuits more effectively. Whether you’re tuning a radio, designing a filter, or working on wireless communication, knowing how resonance works gives you more control over your circuit’s behavior.