CBSE Class 12 · 2016 · Delhi · Alternating CurrentVery Short Answer

Define the 'quality factor' of resonance in a series LCR circuit. What is its S.I. unit?

Answer: Quality factor $Q = \frac{ω _{0} L}{R} = \frac{1}{R} \frac{L}{C}$ ; it is a pure number and has no unit.

Solution

The quality factor

Q

of a series LCR circuit measures the sharpness of resonance; it is the ratio of the voltage across the inductor (or capacitor) at resonance to the applied voltage, equal to

Q = \frac{ω _{0} L}{R} = \frac{1}{ω _{0} C R} = \frac{1}{R} \frac{L}{C}

where

ω_{0} = 1/ L C

is the resonant angular frequency. Being a ratio of like quantities,

Q

is dimensionless and has

no unit

CBSE Class 12 Board · 2016 · Delhi · Subjective

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