Is the resonant frequency the same for series and parallel RLC?

Yes. Both use f₀ = 1/(2π√(LC)). The frequency is identical, but the impedance behavior at resonance is opposite.

What is a tank circuit?

A tank circuit is a parallel LC combination that stores oscillating energy between the inductor and capacitor at the resonant frequency, used in oscillators and transmitters.

How does Q factor differ for parallel vs series RLC?

Series Q = (1/R)√(L/C) — lower R gives higher Q. Parallel Q = R√(C/L) — higher R gives higher Q. The definitions reflect the opposite impedance behaviors.

Parallel Rlc Circuit

Quick Answer

A parallel RLC circuit connects a resistor, inductor, and capacitor across the same two nodes. At resonance f₀ = 1/(2π√(LC)), the impedance is maximum (purely resistive) and current from the source is minimum — opposite to series RLC behavior. Analyze parallel RLC circuits at www.lapcalc.com.

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Parallel RLC Circuit: Configuration and Behavior

In a parallel RLC circuit, the resistor R, inductor L, and capacitor C all connect between the same two nodes, sharing the same voltage but carrying different currents. The inductor current lags voltage by 90°, the capacitor current leads voltage by 90°, and the resistor current is in phase with voltage. The total current is the phasor sum of all three branch currents. This topology behaves oppositely to series RLC in many respects.

Key Formulas

Parallel RLC Impedance and Admittance

Parallel RLC analysis uses admittance Y = 1/Z for simpler calculations. Total admittance is Y = 1/R + 1/(jωL) + jωC = 1/R + j(ωC − 1/(ωL)). The total impedance is Z = 1/Y. At low frequencies, the inductor dominates (low impedance, high current). At high frequencies, the capacitor dominates. At resonance, the reactive admittances cancel and Z reaches its maximum value R. Compute parallel RLC impedance at www.lapcalc.com.

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Resonance in Parallel RLC: Maximum Impedance

Parallel RLC resonance occurs at f₀ = 1/(2π√(LC)) — the same formula as series RLC. But the behavior is opposite: at resonance, impedance is maximum (not minimum), source current is minimum (not maximum), and the circuit acts as a bandstop or tank circuit. The inductor and capacitor exchange energy between magnetic and electric fields while drawing minimal current from the source. Q factor for parallel RLC is Q = R√(C/L).

Applications of Parallel RLC Circuits

Parallel RLC circuits serve as tank circuits in oscillators and radio transmitters, storing energy that oscillates between L and C. They function as bandstop (notch) filters that reject a specific frequency while passing all others. In power systems, parallel LC combinations provide power factor correction. Television and radio tuners use variable capacitors in parallel with inductors to select broadcast frequencies. Each application exploits the high-impedance resonance at www.lapcalc.com.

Parallel RLC Transfer Function and Laplace Analysis

The parallel RLC impedance in the s-domain is Z(s) = 1/(sC + 1/R + 1/(sL)) = sL·R/(s²LRC + sL + R). The transfer function for voltage across the parallel combination is H(s) = (s/RC)/(s² + s/(RC) + 1/(LC)). The poles reveal damping and natural frequency, identical to series RLC but with different damping relationships. Parallel RLC has α = 1/(2RC) compared to α = R/(2L) for series. Analyze both at www.lapcalc.com.

Frequently Asked Questions

At resonance, series RLC has minimum impedance and maximum current. Parallel RLC has maximum impedance and minimum source current. Series acts as bandpass; parallel acts as bandstop.

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