Question

For a given series LCR circuit, the term

\(\frac{1}{R}\sqrt{\frac{L}{C}}\)

(1) is a dimensionless term that provides a measure of (i) the quality factor (Q) and (ii) the power factor of the circuit at resonance

(2) is a dimensionless term that provides a measure of (i) the sharpness of resonance (S) and (ii) the voltage magnification of the circuit at resonance

(3) is a dimensional term that provides a measure of the (i) voltage magnification of the circuit at resonance and (ii) the sharpness of resonance (S) of the circuit

(4) is a dimensionless term that provides a measure of (i) the sharpness (S) of resonance the circuit and (ii) the quality factor (Q) of the circuit

Answer 1

(4) is a dimensionless term that provides a measure of (i) the sharpness (S) of resonance the circuit and (ii) the quality factor (Q) of the circuit

For a series LCR circuit, the sharpness of resonance (S), the quality factor (Q) and the voltage magnification, at resonance, are all measureing through the term \(\frac{ω_0L}{R}\). The resonant frequency ω₀ , being equal to 1/LC, this term is equivalent to the term \(\frac{1}{R}\sqrt{\frac{L}{C}}.\) 

This term is a dimensionless term (because ω₀L as well as R both have the dimensions of impedance). (The power factor, of the circuit, at resonance, equals 1; it is not equal to this term).