Question 1

What is electrical resonance in an RLC circuit?

Accepted Answer

Resonance occurs when the inductive reactance and capacitive reactance cancel exactly, so the circuit's impedance equals just the resistance R. The current driven by an AC source then reaches its maximum value.

Question 2

What is the resonant frequency formula?

Accepted Answer

The resonant angular frequency is ω0 = 1/√(LC), giving a resonant frequency f0 = 1/(2π√LC). It depends only on the inductance L and capacitance C, not on the resistance.

Question 3

How is the impedance of a series RLC circuit calculated?

Accepted Answer

Impedance is Z = √(R² + (ωL − 1/(ωC))²). The term ωL is the inductive reactance and 1/(ωC) is the capacitive reactance; their difference is the net reactance.

Question 4

What is the Q factor?

Accepted Answer

The quality factor Q = ω0·L/R measures how sharp the resonance peak is. A high Q means low resistance, a narrow bandwidth and a tall, selective resonance curve.

Question 5

Why does current peak at resonance?

Accepted Answer

Because the inductive and capacitive reactances cancel, the impedance drops to its minimum value R. Since current amplitude I = V/Z, minimum impedance produces maximum current.

Question 6

What happens to the phase at resonance?

Accepted Answer

At resonance the voltage and current are in phase (phase angle φ = 0). Below resonance the circuit is capacitive (current leads); above resonance it is inductive (current lags).

Question 7

How does resistance affect the resonance curve?

Accepted Answer

Higher resistance lowers and broadens the resonance peak (low Q), while lower resistance produces a taller, sharper peak (high Q). Resistance sets the bandwidth Δf = f0/Q.

Question 8

How is this used in radio tuning?

Accepted Answer

A tuned RLC circuit responds strongly only to signals near its resonant frequency. Varying C (or L) shifts f0 so the receiver selects one station while rejecting others.

Question 9

What is the bandwidth of an RLC resonator?

Accepted Answer

The bandwidth is the frequency range between the half-power (−3 dB) points where current falls to 1/√2 of its peak. It equals Δf = f0/Q = R/(2πL).

Question 10

What is a phasor diagram?

Accepted Answer

A phasor diagram represents the AC voltages across R, L and C as rotating vectors. Adding the phasors shows the total voltage and the phase difference between voltage and current.

📻 RLC Resonance — Driven Electrical Oscillator

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