Question

State the condition for resonance to occur in a series LCR a.c. circuit and derive an expression for the resonant frequency. 

Draw a plot showing the variation of the peak current (i_m) with frequency of the a.c. source used. Define the quality factor, Q of the circuit. 

Calculate the (i) impedance, (ii) wattless current of the given a.c. circuit

Answer 1

Condition for resonance to occur in series LCR ac circuit: For resonance the current produced in the circuit and emf applied must always be in the same phase

The graph of variation of peak current im with frequency is shown in fig. Half power frequencies are the frequencies on either side of resonant frequency for which current reduces to half of its maximum value. In fig. f₁ and f₂ are half power frequencies. 

Quality Factor (Q) : The quality factor is defined as the ratio of resonant frequency to the width of half power frequencies.