Q127 / 180 · AIIMS 2012 · Physics

In a given series $L C R$ circuit $R=4 \Omega, X_L=5 \Omega$ and $X_C=8 \Omega$, the current

  • Correct answer
    A
    Leads the voltage by $\tan ^{-1}(3 / 4)$.
  • B
    Leads the voltage by $\tan ^{-1}(5 / 8)$.
  • C
    Lags the voltage by $\tan ^{-1}(3 / 4)$.
  • D
    Lags the voltage by $\tan ^{-1}(5 / 8)$.

Solution

The phase angle $\theta=\tan ^{-1}\left(\frac{X_C-X_L}{R}\right)$ $=\tan ^{-1}\left(\frac{8-5}{4}\right)$ $\theta=\tan ^{-1}\left(\frac{3}{4}\right)$ Therefore, the current leads the voltage by $\tan ^{-1}\left(\frac{3}{4}\right)$

Hence, the correct answer is option: 'A'.

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