What Is Sharpness Of Resonance - Q Factor Of RLC Circuit, Coil (2024)

FAQs

What Is Sharpness Of Resonance - Q Factor Of RLC Circuit, Coil? ›

Q-Factor in a Series RLC Resonant Circuit

What is the sharpness of resonance? The sharpness of resonance is defined using the Q factor which explains how fast energy decay in an oscillating system is. The sharpness of resonance depends upon: Damping: Effect due to which there is a reduction in amplitude of vibrations.

An important property of oscillating systems like RLC circuits is the Q factor, which quantifies the strength of damping in the system. The Q factor is inversely proportional to the resistance for a series RLC circuit but increases with the resistance in a parallel RLC circuit.

The sharpness of the resonance is measured using the Q factor, which quantifies how quickly energy decays in an oscillating system. As damping increases or decreases, the sharpness of resonance increases or decreases, and as the amplitude expands, the sharpness of resonance reduces.

Q factor is alternatively defined as the ratio of a resonator's centre frequency to its bandwidth when subject to an oscillating driving force. These two definitions give numerically similar, but not identical, results. Higher Q indicates a lower rate of energy loss and the oscillations die out more slowly.

If the Quality factor is low such as 0.1 to 5, the curve is broad and its peak is not sharp. If Q is high such as 10 , the curve becomes narrow and its peak is narrow. If Q is very high and increasing from 100 to 100k , the curve becomes very narrow and its peak is very sharp.

Quality factor of resonance is a dimensionless parameter that describes how underdamped an oscillator or resonator is, and characterizes a resonator bandwidth relative to its center frequency. At resonance, XC=XL ⟹wo=√1LC. ∴ Quality factor in series LCR circuit Q=woLR=1R√LC.

Quality factor (Q) or coil Q-factor is a dimensionless unit for the losses of a coil, quartz, or a resonator. For coils this refers to the ohmic losses of the coil-wire. They are inversely proportional for the coil quality and are calculated from the ratio of reactance to ohmic resistance.

∴Q=1√LC⋅LR=1R√LC. For series L-C-R circuit, resonant frequency is ω0.

The Q, or quality, factor of a resonant circuit is a measure of the “goodness” or quality of a resonant circuit. A higher value for this figure of merit corresponds to a more narrow bandwidth, which is desirable in many applications.

What is resonance in an RLC circuit? ›

The resonance of a series RLC circuit occurs when the inductive and capacitive reactances are equal in magnitude but cancel each other because they are 180 degrees apart in phase. The sharp minimum in impedance which occurs is useful in tuning applications.

Therefore, the power factor of an LCR circuit at resonance is 1. Note: At resonance, the LCR circuit behaves like a purely resistive circuit and the effects of the capacitor and inductor cancel each other out.

Resonance occurs when the value of inductive and capacitive reactances have equal magnitude but a phase difference of 180°. In this condition, they cancel each other. This is known as the resonance frequency of a series LCR circuit. Thus, the circuit is a resonance LCR circuit.

The quality factor is a ratio of resonant frequency to bandwidth. It relates the maximum or peak energy stored in the circuit (the reactance) to the energy dissipated (the resistance) during each cycle of oscillation. The higher the circuit Q, the smaller the bandwidth.

Significance : Q factor determines the sharpness of the resonance curve, if Q is high, the resonance curve is sharper and the energy lost by the circuit is less. Sharpness: Sharpness of a AC circuit is related to the Q factor. IF the sharpness is more we get a clear effect in the system and resistance is less.

Assertion (A) : Quality factor of a series LCR circuit is Q=1R√LC. Reason (R) : As bandwidth decreases, Q increases in a resonant LCR circuit.

The factor equals 2 times the number of oscillation periods required for the stored energy to decay to (≈ 37%) of its initial value. The factor of an optical resonator equals the finesse times the optical frequency divided by the free spectral range.

In this case, the quality factor can be determined from the Fourier transform of the field by finding the resonance frequencies of the signal and measuring the full width half maximum (FWHM) of the resonant peaks. We can then use Q = f_R/f where f_R is the resonant frequency and f is the FWHM.

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