An alternating emf $$\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}$$ volt is applied to a capacitor of $$2 \mu \mathrm{F}$$, the rms value of current in the circuit is ________ $$\mathrm{mA}$$.

If the net electric field at point $$\mathrm{P}$$ along $$\mathrm{Y}$$ axis is zero, then the ratio of $$\left|\frac{q_2}{q_3}\right|$$ is $$\frac{8}{5 \sqrt{x}}$$, where $$x=$$ ________.

Two slits are $$1 \mathrm{~mm}$$ apart and the screen is located $$1 \mathrm{~m}$$ away from the slits. A light of wavelength $$500 \mathrm{~nm}$$ is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the single slit pattern is __________ $$\times 10^{-4} \mathrm{~m}$$.

A potential divider circuit is connected with a dc source of $$20 \mathrm{~V}$$, a light emitting diode of glow in voltage $$1.8 \mathrm{~V}$$ and a zener diode of breakdown voltage of $$3.2 \mathrm{~V}$$. The length (PR) of the resistive wire is $$20 \mathrm{~cm}$$. The minimum length of PQ to just glow the LED is _________ $$\mathrm{cm}$$.