Question

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

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{4}$
• C. zero
• D. nothing can be said

Answer 1

Answer: (C)

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