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Consider the circuit shown in the figure. In this circuit $R=1 k\Omega$, and $C=1 \mu F$. The input voltage is sinusoidal with a frequency of $50$ Hz, represented as a phasor with magnitude $V_{i}$ and phase angle $0$ radian as shown in the figure. The output voltage is represented as a phasor with magnitude $V_{0}$ and phase angle $\delta$ radian. What is the value of the output phase angle $\delta$ (in radian) relative to the phase angle of the input voltage?

- $0$
- $\pi$
- $\frac{\pi}{2}$
- $-\frac{\pi}{2}$

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