Question

The amplitude of current in series LCR circuit connected to an AC of frequency "?" is given by im = vm / ?(R^2 + (XL - XC)^2) where XL and XC are inductive and capacitative reactances respectively and "vm" is amplitude of voltage. Starting from this equation show that sharpness of resonance in the circuit is equal to the quality factor of the circuit.

          The amplitude of current in series LCR circuit connected to an AC of frequency "?" is given by
im = vm / ?(R^2 + (XL - XC)^2)
where XL and XC are inductive and capacitative reactances respectively and "vm" is amplitude of voltage. Starting from this equation show that sharpness of resonance in the circuit is equal to the quality factor of the circuit.

The amplitude of current in series LCR circuit connected to an AC of frequency "?" is given by
im = vm / ?(R^2 + (XL - XC)^2)
where XL and XC are inductive and capacitative reactances respectively and "vm" is amplitude of voltage. Starting from this equation show that sharpness of resonance in the circuit is equal to the quality factor of the circuit.

Added by Karl I.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

01/13/2023

Step 1

Step 1: Start with the given expression for the amplitude of current in a series LCR circuit: \[ i_m = \frac{V_m}{\sqrt{R^2 + (X_L - X_C)^2}} \] Show more…

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The amplitude of current in a series LCR circuit connected to an AC of frequency "ω" is given by im = vm / √(R^2 + (XL - XC)^2), where XL and XC are inductive and capacitive reactances respectively, and vm is the amplitude of voltage. Starting from this equation, show that the sharpness of resonance in the circuit is equal to the quality factor of the circuit.