An arc lamp requires a direct current of $10\ A$ at $80\ V$ to function. If it is connected to a $ 220\ V (rms ), 50\ Hz\ AC$ supply, the series inductor needed for it to work is close to :

A circuit element $X$ when connected to an a.c. supply of peak voltage $100\,V$ gives a peak current of $5\,A$ which is in phase with the voltage. A second element $Y$ when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by $\frac{\pi}{2}$. If $X$ and $Y$ are connected in series to the same supply, what will be the rms value of the current in ampere?

In $LC$ circuit the inductance $\mathrm{L}=40\; \mathrm{mH}$ and capacitance $\mathrm{C}=100\; \mu \mathrm{F} .$ If a voltage $\mathrm{V}(\mathrm{t})=10 \sin (314 \mathrm{t})$ is applied to the circuit, the current in the circuit is given as 

The value of the current through an inductance of $1H$ and of negligible resistance, when connected through an $ac$ source of $200 \,V$ and $50 \,Hz$ is

An inductive circuit contains resistance of $10$ $\Omega$  and an inductance of $20\, H$. If an $ac$ voltage of $120 \,V$ and frequency $60\, Hz$ is applied to this circuit, the current would be nearly