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  4. For a series LCR circuit, the phase difference between current and voltage at the condition of resonance will be :

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Q. For a series LCR circuit, the phase difference between current and voltage at the condition of resonance will be :

Bihar CECEBihar CECE 2003Alternating Current

Solution:

In a series LCR circuit, potential difference leads the current by an angle $\phi$ (let).
$\phi=\tan ^{-1}\left(\frac{X_{L}-X_{C}}{R}\right)$
or $\phi=\tan ^{-1}\left(\frac{\omega L-\frac{1}{\omega C}}{R}\right)$
At resonance, $X_{L}=X_{C}, i . e, \omega L=\frac{1}{\omega C}$
Hence,$\phi=\tan ^{-1}(0)=0$
Therefore, phase difference between current and voltage at resonance is zero.