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For an RLC circuit driven with voltage of amplitude v m and frequency ω 0 = 1 L C the current exhibits resonance. The quality factor, Q is given by

Options

  1. AC R ω 0
  2. Bω 0 L R
  3. Cω 0 R L
  4. DR ( ω 0 C )

Correct answer

B. ω 0 L R

Step-by-step solution

The quality factor of an L.C.R. circuit is given by, (Quality factor) Q = 1 R L C . . . ( i ) Where L , R , C are the inductance, resistance, and conductance of the L.C.R. circuit. The given resonance frequency is, ω 0 = 1 L C ⇒ C = 1 ω 0 L     . . . ( ii ) From ( i ) and ( ii ) ⇒ Q = 1 R L × ω 0 L ⇒ Q = ω 0 L R

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