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?
1. $0$
2. $\pi$
3. $\frac{\pi}{2}$
4. $-\frac{\pi}{2}$