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(D) The impedance $Z$ of an $LCR$ series circuit is given by the formula: $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $X_L = \omega L = 2\pi f L$ and $X_C

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first decreases, becomes minimum and then increases

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(D) The impedance $Z$ of an $LCR$ series circuit is given by the formula: $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $X_L = \omega L = 2\pi f L$ and $X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}$.As the frequency $f$ increases, the inductive reactance $X_L$ increases linearly, while the capacitive reactance $X_C$ decreases.At low frequencies, $X_C$ is dominant, so $Z$ decreases as $f$ increases.At the resonant frequency $f_0 = \frac{1}{2\pi \sqrt{LC}}$, $X_L = X_C$, making the impedance $Z = R$, which is the minimum possible value.As the frequency increases further beyond $f_0$, $X_L$ becomes dominant, causing the impedance $Z$ to increase again.Therefore, the impedance first decreases, reaches a minimum at resonance, and then increases.

With a gradual increase in the frequency of an $A.C.$ supply, the impedance of an $LCR$ series circuit

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