Consider a series LCR circuit whose squared impedance is written as a function of…
PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Consider a series LCR circuit whose squared impedance is written as a function of angular frequency.
(i) Write this expression for the squared impedance without simplification.
(ii) Differentiate it with respect to angular frequency and establish the condition for which the first derivative vanishes. Interpret the physical significance of this result.
(iii) Evaluate the second derivative at the frequency found in part (ii) and hence show that the impedance attains a minimum value there.
(iv) Discuss qualitatively how increasing or decreasing the resistance of the circuit affects the sharpness of the resonance curve.