For the LCR AC circuit (resonance frequency ωo) shown in the figure below, choose the correct statement(s).

List 1	List 2
(i) ω0	a) depends on L,C
(ii) At ω =ω0 , VR is	b) independent of L, C
(iii) VR and I are	c) In phase
(iv)  At ω =ω0 /2, VR is	d) Out of phase

 

Concept :
This problem deals with the concept of resonance in an RLC circuit (Resistor inductive capacitor circuit). At the resonance frequency, the inductive reactance and capacitive reactance are equal, resulting in a minimum impedance and a maximum current. Resonance in an RLC circuit is defined by the resonant frequency , at which the circuit naturally oscillates.

The formulas involved are:
Resonant frequency ,
Impedance ,
At resonance, , making Z = R (minimum impedance),
The phase angle

At resonance, , so the phase angle phi = 0 , and the current and voltage are in phase.

Solution :

At resonance frequency :

The total impedance Z at resonance becomes:

Thus, the impedance is at a minimum .

The phase angle is given by:

This means that at resonance, the current and voltage are in phase.

Finally, the voltage across the resistor is independent of the values of L and C because at resonance, .
At resonance, the impedance is minimized, and the current and voltage are in phase.