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

Step-by-step solution

The impedance of an LCR series circuit is given by Z = R^2 + (X_L - X_C)^2 where X_L = 2 f L and X_C = 1 2 f C . At low frequencies, X_C > X_L , so the impedance is high. As the frequency f increases, X_C decreases and X_L increases, which reduces the magnitude of (X_L - X_C) . Thus, the impedance decreases. At the resonant frequency f = 1 2 LC , X_L = X_C , and the impedance becomes minimum, Z = R . With a further increase in frequency, X_L > X_C , and the magnitude of (X_L - X_C) increases, causing the impedance