To light, a $50 \mathrm{~W}, 100 \mathrm{~V}$ lamp is connected, in series with a capacitor of capacitance $\frac{50}{\pi \sqrt{x}} \mu F$, with $200 \mathrm{~V}, 50 \mathrm{~Hz} \,\mathrm{AC}$ source. The value of $x$ will be ___________.