A 110 V, 50 Hz, AC source is connected in the circuit (as shown in figure). The current through the resistance 55 Ω, at resonance in the circuit, will be _________ A.

Concept: 

In this resonance condition is used which is known as:

When the magnitude of the inductive and capacitive resistance values is equal but have a 180° phase difference, resonance occurs in LCR series circuits. This is referred to as an LCR circuit's resonance frequency.

At resonance, \( \omega = \frac{1}{\sqrt{LC}}\) we know, X_c = XL    -----(1)

Here, \( \frac{1}{Z} = \sqrt{[\frac{1}{X_{c}} - \frac{1}{X_{L}}]^{2}} \)      -----(2)

Where Z = impedance of the circuit. 

Solution:

Given:

Using equations (1) and (2) we get: 1/Z = 0 so that Z = ∞ 

Here we get impedance of circuit = ∞ 

We know impedance ∝ 1/current

So current through circuit = 0 A

Hence, the correct answer is 0